help-49

[twilit jetty]

what name does it have?

-2 something -1 is the same as -2 subtract 1

[sly cape]

mixing together the numbers?

[twilit jetty]

its name is addition

its purpose is to mix numbers together

its purpose is not to make them more positive

[sly cape]

well addition always have positive affect..

[twilit jetty]

no it doesnt

you can "add on debt" for example

think of the concept of "more lower"

addition has the effect of combining things together

youve been working with positive numbers for so long that you think addition can only ever make things higher

with negative numbers, this is no longer the case

think about the rules youre using in the first place to simplify -2 + -1

[sly cape]

okay its obviosuly -3?

[twilit jetty]

if the + sign must make things larger, then why did you end up simplifying it to a smaller number?

the rules are correct, you know that

this is clearly an example where adding -2 and -1 ends up being -3

before it was -2 and -1, after it was -3

[sly cape]

yeah with negative affect..

[twilit jetty]

yes, and there you can see that addition, or adding, as denoted by the plus sign,

has just produced a number smaller than what came before it

this is part of the structure we use to add numbers together

addition doesnt mean positive

the unary operator +, as in +4, means positive instead

youve just mistook one for the other

[sly cape]

yeah but adding numbers is getting the results higher but in this case it isnt

so it is subracting.

[twilit jetty]

well contrary to your beliefs, the rest of the world uses negative numbers and adding them a different way

having to remove particular aspects that you expect out of certain operators is part of what allows us to use them in very general situations

[sly cape]

theres no need for + to exist in -2 + -1

[twilit jetty]

lets consider for example, -2 + x

would you say the -2 and x are being added together?

what?

[sly cape]

nvm

[lavish venture]

which is why we frequently omit it?

[twilit jetty]

you literally just told me earlier on that that is not how we read it

here

[sly cape]

uh yes?

[twilit jetty]

thats dangerous

what if x is -1?

would you still call it adding?

and if the + sign can no longer be called "adding," what else are we going to call it?

[sly cape]

in which case?

[twilit jetty]

in the expression -2 + x,
would the + be considered adding if the x is -1?

[sly cape]

no its not

[twilit jetty]

now in the expression -2 + -1, would the + still be considered adding?

see there, youve changed your mind

[sly cape]

yes

[twilit jetty]

and this is important: theres an important aspect of math called "consistency"

[sly cape]

youre gaslighting me i think

[twilit jetty]

Im convincing you that thinking -2 + -1 isnt addition is a terrible idea

now Im going to tell you how we usually treat these operators, so you can compare the ideas together

so far youre viewing the operators in terms of what they will end up doing

[sly cape]

it isnt an addition

[twilit jetty]

the idea here is that we should be able to use the same symbol or name for the same kind of action, not the same kind of output

[sly cape]

okay can we like go back to the topic and not argue what is an addition or not?

[twilit jetty]

oval, this is a very important distinction

both this and the -x^2 are two separate but still important issues

[lavish venture]

how do you define +?

[twilit jetty]

you cant just drop one instead of the other

[sly cape]

mixing two subjects that will result into a greater result than before.

[twilit jetty]

does + always have to give you a greater result than before?

[sly cape]

otherwise what would it be?

[lavish venture]

oh so like 2 times 3

[twilit jetty]

we would still call it addition, its just no longer an aspect that addition does anymore

the core difference here is what we decide to keep when -2 + -1 is -3

[sly cape]

yeah so it a subtraction, more negative result

[twilit jetty]

youre keeping the "greater than before" part

we keep the "Im typing a + sign" part

commonly addition refers to the specific tool, action, symbol, verb, process you are doing

instead of the output

[sly cape]

Theres a difference between a language and actual math

[twilit jetty]

I use a + sign, I am adding, even if that adding acts opposite to what I expect

[waxen musk]

what even is the topic at hand here? we put 3*(-2) so its easy to read, although it is okay to put 3*-2

[twilit jetty]

lets say I am $5 in debt

if I add on $2 in debt, how much debt do I have?

[sly cape]

-$7?

[twilit jetty]

right,

now lets say instead I am trying to make a profit, but I've already lost $5

[sly cape]

which is less than -$5

[twilit jetty]

if I lose an __addition__al $2, I would be -$7 below where I started

[scenic wyvern]

may I provide perhaps another viewpoint?

[twilit jetty]

try

[scenic wyvern]

if I may interrupt, maybe one way of thinking about addition/subtraction and positive/negative numbers is like this.
think about positive numbers as moving to the right on a number line, and think of negative numbers as moving to the left (with right being bigger).
now, addition means to move in the same direction as the number, and subtraction is to move in the opposite direction from the number.

so adding a negative number means to move in the same direction as the negative number = move left.
and subtracting a negative number means to move in the opposite direction from the negative number = move opposite of left -> move right.

[sly cape]

so its not an addition but subtraction

[waxen musk]

$$a+(-b)=a-b$$

[grand pond]

Cycadellic

[twilit jetty]

I dont have strong hopes, but see if youre convinced by hanako's view of addition

[waxen musk]

where (-b) is negative b

[sly cape]

ill read that in a moment

[twilit jetty]

please read it right now

hanako put some effort into typing it

you can hear them out at least

[sly cape]

but @twilit jetty if you do 6-3 thats also a subtraction

[waxen musk]

mtt's point here is that the addition of a negative number is the subtraction of a positive number, and there is a good and relatively simple proof of this too

[twilit jetty]

that isnt my point, actually

because it depends on an assumption oval cannot agree with

[waxen musk]

oh, sorry

what is this assumption?

[sly cape]

subtracting a negative number means to move in the opposite direction from the negative number = move opposite of left -> move right.
but -2-2 is going to the left side, not right

[scenic wyvern]

you're subtracting a positive number.

[twilit jetty]

aaaand it didnt even survive past the first hurdle, sorry hanako

the point here is that oval thinks addition should only produce larger numbers and subtraction should only produce smaller number

this is true when we are working with positive numbers

however, when negative numbers are introduced,

[waxen musk]

@sly cape do you understand and agree with this statement here?

[twilit jetty]

something needs to be redefined

[lavish venture]

the major misconception you're having is that subtraction/division aren't the fundamental operations. we adopt shorthand notation like
x - y which is definitionally x + (-y) where the symbol "-y" is defined to be the additive inverse of y meaning it is the number that when added to y gives 0. we write x - y for notational convenience. addition has nothing to do with getting larger. you'll notice that in your shaky definition of addition you said you mix two things and get a larger thing and i pointed out that multiplying by numbers > 1 has this exact effect as well, as does many other things. maybe learn how addition is formally defined first.

[sly cape]

no its a * -b

[twilit jetty]

I think we have too many cooks here all saying similar ideas

[waxen musk]

this is a very different thing, how did you arrive at this?

[scenic wyvern]

I'll leave it to you folks, sorry for interrupting

[sly cape]

bracket nearby so multiplication

[twilit jetty]

theres a + sign there though

[waxen musk]

3 * (-2) = -6
whereas
3 + (-2) = 1

[twilit jetty]

brackets can mean more than just multiplication, it could just be to do the first thing you see

[lavish venture]

3 * (-2) = -2

[twilit jetty]

3 + (-2) is 3 + -2

[lavish venture]

🤔

[twilit jetty]

the - is just to show that the 2 is negative, and thats being done first there

[waxen musk]

sorry

[twilit jetty]

next is 3 + -2 to get 1

[lavish venture]

happens

[twilit jetty]

if you had 3(-2) instead, then that would be -6

as you can see, theres no operator between the 3 and the -2

[sly cape]

3 + (-2) = 1
yeah so subtraction

[waxen musk]

exactly

[twilit jetty]

cool, lets get back on topic

[waxen musk]

3 + (-2) = 3 - 2

[twilit jetty]

alright oval what I want to do here is make clearer how we see things

[sly cape]

but someone told that numbers near a bracket = multiplication even mtt said that

and you change signs only when theres a minus

[twilit jetty]

oval theres more to these rules than just feelings

3 + (-2) isnt "near enough"

[waxen musk]

they meant specifically without an operation, so 3(-2) = 3 * (-2) only

[twilit jetty]

you need to have a crystal clear idea before we do this

[sly cape]

well either maths is about logic or "exceptional rules"

[twilit jetty]

theres no exceptions here

[sly cape]

well you guys are doing it

[twilit jetty]

oval

listen to me

3 + (-2)

and 3 (-2)

an entire + sign is missing

so theyre different, arent they

thats like comparing 3 * 2 with 32

[sly cape]

yeah but youre putting it in a bracket

[twilit jetty]

oval, theres a common way to write multiplication, which is with no symbol at all

for example, xy means x * y

[twilit jetty]

if no operator is written, multiplication is assumed

[sly cape]

ik that..

[twilit jetty]

that is where the * comes from

[sly cape]

i know that..

[twilit jetty]

using brackets is how we can create a lack of operator

but it is not the only purpose

brackets can also mean just doing something first

in 3 + (-2) for example,

there is still an operator (+) between the 3 and the (-2)

it does not mean you "transform" the + to a *

[twilit jetty]

there was supposed to be a missing operator for multiplication to happen

[sly cape]

why

[twilit jetty]

3 + (-2) has an operator between the 3 and the (-2), which is the +
3 - (-2) has an operator between the 3 and the (-2), which is the -
3 / (-2) has an operator between the 3 and the (-2), which is the /

[sly cape]

ok lets go to the point..

[twilit jetty]

3(-2) does not have an operator between 3 and the (-2)

and so we view that as 3 * (-2)

[sly cape]

so 3+(-2) is 1 and 3(-2) is -6

okay

i get it

[twilit jetty]

very good, that trips people up

theres a good reason for that actually

often times we consider things multiplied together to be part of a "term"

[sly cape]

ok lets go to the exponents

[twilit jetty]

oval uh

that you still think addition needs to produce larger numbers is suspect

we aint getting far if youre still thinking that

[sly cape]

But you can't deny it.

Thats the point

[twilit jetty]

tell me

why does addition need to produce larger numbers?

[sly cape]

"add"

[waxen musk]

addition with a positive number does do this, but addition with a negative number should produce a smaller result

[twilit jetty]

when I add on debt, I end up at a lower standing than I did before

[lavish venture]

mtt i think hes being obtuse

[twilit jetty]

this guy doesnt seem trolly enough to even do that

[waxen musk]

likewise, addition with 0 doesnt change anything

[lavish venture]

idk man..

[sly cape]

i have 5 apples how many do i need to bake the pie

thats the meaning

[lavish venture]

ive read through this conversation

[sly cape]

what is obtuse

[twilit jetty]

yes, its a long line of "Im trying to make a point but X, Y, Z get in the way"

[lavish venture]

sure

[twilit jetty]

oval you can just agree that youre not comfortable with negative numbers

[sly cape]

obtuse can be an angle

[lavish venture]

yep

[twilit jetty]

and that they make + and - signs do strange things

[lavish venture]

👍

[waxen musk]

say
a<0
add b to both sides
a+b<b
it just got smaller after an addition

[twilit jetty]

knief is accusing you of deliberately being unclear to trip me up

[sly cape]

but i KNOW how negative numbers work

[twilit jetty]

you just dont agree with the language?

[sly cape]

we'll ive said many times to go to the main point but you seem to be focused on this 'adding problem'

[twilit jetty]

well yes

because this is very closely tied to the -x^2

the main problem here is reading the symbols

and you dont seem to agree with the usual way to do it

[twilit jetty]

so if you just state that you dont agree with the way things are called,

[sly cape]

thats because 0 is already bigger than a

[twilit jetty]

oval dont engage

no progress will be made if you dont address the adding problem directly

[waxen musk]

mhm, so if a is negative, then an addition makes it smaller

[twilit jetty]

lets look at the broader picture here alr

you just dont agree that addition can make smaller numbers, so when it does, theres always a reason why addition seemed to fail at its job

[sly cape]

then its called subtraction

[twilit jetty]

for example, in -5 - -5,

that would be addition to you, because -5 - -5 = -5 + 5 = 0, right?

its ultimatley addition

[sly cape]

NEGATIVE number makes numbers smaller

[waxen musk]

...and the addition of a negative number is the subtraction with that positive number

[twilit jetty]

no it doesnt

here a negative number made a number larger

[sly cape]

but you cant add two negative signs lol

[twilit jetty]

aha

[sly cape]

in any equation

[twilit jetty]

so what are we going to do with --5 then

[sly cape]

double subtracting?

[twilit jetty]

and what would it do?

[sly cape]

subtract

turn into more negative number

[twilit jetty]

interesting idea

now what would this number actually do?

[sly cape]

i might find a thing/rule in mathematics

[sly cape]

Wdym? Subtract

[twilit jetty]

thats the same mathematics that calls -2 + -1 adding though

surely we can figure out what --5 is

is it the same as 5? -5?

[sly cape]

Well this is adding

[twilit jetty]

ok I have an idea for you

so far you agree that x + -x is always 0, right

lets test it

[sly cape]

okay

yes

[twilit jetty]

very suddenly changed your mind there

in a way thats a good sign

you doubted, tested, then confirmed

we can do the same to see the nature of --5

[twilit jetty]

the idea here is to use a fundamental rule in mathematics: we should be able to put anything in x here

since this should be true "for all x"

now lets try this for x = -5, and we get:

-5 + --5 = 0

so whatever this --5 is, it must turn -5 to 0 by adding

however, -5 + 5 = 0 also

-5 + 5 = 0
-5 + --5 = 0

does this convince you that 5 and --5 are the same?

[sly cape]

but double minus doesnt exist

[twilit jetty]

suppose it does

if it did exist, would it act like 5 in this example?

[sly cape]

id say no as it would just result into being -5

[twilit jetty]

look closer at the place --5 is at in the expression

[sly cape]

no wait

[twilit jetty]

-5 + 5 = 0

[sly cape]

-0

[twilit jetty]

-5 + --5 = 0

they are both numbers where, if you add it to -5, you will end up with 0

[sly cape]

okay -10

[twilit jetty]

oval, if you had x + -x = 0

[fathom onyx]

-# I think the preliminary thing to learn here is whether -0 = 0 (which it does, but I'm not sure that's clear to Oval)

[twilit jetty]

and x was -5

then that means -5 + --5 = 0 too

[sly cape]

but then the minus will just disappear

[twilit jetty]

wdym minus?

stick to what we are accepting is true here

[sly cape]

--5

[twilit jetty]

so youd rather trust your feelings on this one?

--5 shouldnt be 5, because the minuses both disappear?

[sly cape]

idk how i would even solve it but id just thing it was -10

[twilit jetty]

ever heard of a double negative?

like here for example

its a common idea

not just in math

--5 is an example of a double negative

double negative things exist

[sly cape]

that is smart

but - * - = +

but that is just +

[twilit jetty]

and?

so --5 is +5 then

[sly cape]

-(-5+5)

-5

[twilit jetty]

-(-5 + 5) is -0

not -5

-5 + 5 is 0,

so -(-5 + 5) is -0

[sly cape]

right -0

[twilit jetty]

oval you need to be certain on your statements before you state them

[sly cape]

but that results into being undefinied so double negatives don't exist.

[fathom onyx]

@twilit jetty

[twilit jetty]

yep

[sly cape]

-0 doesnt exist.

[twilit jetty]

that means we just need to figure out what -0 should be about

well consider this

0 + -0

what would this be?

and remember, x + -x = 0 is always true for any x

[sly cape]

-0

[twilit jetty]

0 + -0 is -0, sure

[twilit jetty]

now see what happens if you put in x=0 here

what do you get?

[sly cape]

-0

?

[twilit jetty]

x + -x = 0
0 + -0 = 0

[sly cape]

0 and then - 0

[twilit jetty]

so 0 + -0 is also 0 too

that then must mean that 0 and -0 must be equal

0 + -0 = 0 (from x + -x = 0)
0 + -0 = -0 (because adding 0 to anything doesnt change it)

and so we have proven that 0 and -0 must be the same

[sly cape]

yeah but that is exception cause its a zero

[twilit jetty]

now youre pulling out exceptions?

its true that the kind of argument we're doing here would only really work for 0 and -0

but its all we need to prove that 0 and -0 are equal

[sly cape]

im lost on this

cause one would be 0 + 0 = 0

and the other one x + -x = 0 so x+ -0 = 0

[twilit jetty]

we're saying x is 0 in that case, so you have to replace the other x as well

0 + -0 = 0

we have that 0 + 0 = 0, and also 0 + -0 = 0 as well

[sly cape]

okay

[sly cape]

okay

[twilit jetty]

in general, 0 and -0 are considered to be the same

[sly cape]

and whats the meaning behind this

[twilit jetty]

there is something important here

[sly cape]

its really not

[twilit jetty]

only in a pedantic sense

when adding, multiplying them they are the same

in the sense that there is nothing that can tell apart 0 and -0

[sly cape]

if i were to multiply it, one would result into a negative

number

[twilit jetty]

not really

5 * -0 is 0

[sly cape]

still -0

[twilit jetty]

0 + -0 is 0, right

[sly cape]

only in this case

[twilit jetty]

so 5 * (0 + -0) is 5 * 0, right

since both numbers are equal, multiplying them by 5 must also be equal

[sly cape]

yes

[twilit jetty]

then we distribute, this is something you agreed to

5 * 0 + 5 * -0

5 * 0 + 5 * -0 = 5 * 0 (distributing left side)

yes?

[sly cape]

yes

[twilit jetty]

very good

then consider:

5 * 0 + 0 = 5 * 0

5 * 0 + 5 * -0 = 5 * 0

in either case, 0 and 5 * -0 are both acting the same way in an addition sense

[sly cape]

mhm

[twilit jetty]

now we can confirm that 0 and 5 * -0 both act the same way in the multiplicative sense too

you know -5 * 3 is the same as 5 * -3, right

[sly cape]

sure

[twilit jetty]

so similarly 5 * -0 is the same as -5 * 0

and -5 * 0 is just 0 again, since anything * 0 is 0

[sly cape]

sure

yeah

[twilit jetty]

and so -0 acts the same as 0 in both addition and multiplication

and this is where the power of mathematics shows us something else interesting

this is all we need to say that -0 and 0 are identical

you see a lot of mathematics tries to assume as little information as possible

to create the most "general" of results

so a lot of mathematics has already been in the word to say that, for example,

if x + y = x + z, then y = z

and if xy = xz, then either y = z or x = 0

[fathom onyx]

-# I'd advise against introducing algebra like this at this moment tbh

[twilit jetty]

the guy already asked a question no normal person would ask

[fathom onyx]

But this holds, yh

[twilit jetty]

I think theyre already in the mindset

these arent exactly the rules that mathematics begins with, exactly, but its enough

[sly cape]

thats clear

[twilit jetty]

now Im going to warn you

this subject is called abstract algebra

this is colleg-level math that attributes a lot of mathy things to seemingly very arbitrary, abstract ideas

and at a lot of times, you cant predict the next direction a course is going to go when they teach you this

why is this important, why remember that, what about those?

the idea here is that with math at the advanced state that it is, these are important directions that get us farther in more efficient ways

notice here: its not because theyre the most correct

its just the most efficient, or the most commonly accepted, or at times just the easiest way

most compromises in the name of more elegant mathmatics arent pretty

to you, one of those is in how we view addition, and another one of those is in how we view -x^2

see this line here?

the basic structure that we have uses a set of things (for example numbers) and an operation that can combine them

but not much more than that

when we define addition, theres a reason why we define it as "5 + -3 is considered adding 5 + -3"

youll notice here this structure has no concept of size

what if, for example, we need to add 5:00 and -3:00?

[sly cape]

so what i said was actually right?

[sly cape]

this is exceptional

[twilit jetty]

I dont see any exceptions here

I see compromises against common sense, which as it turns out isnt very good at rigor

suppose we need to add
...5555555555
- ...333333333

????????????

as you can see, the usual notions of > and <, or > and <, break down

we only have =

and so why define addition with an extra > notion that we cant even have most the time?

[twilit jetty]

what exactly did you say?

you said many things, most of them were not ideal, but a few are very good

[sly cape]

that when adding a negative number is subtractingg

[twilit jetty]

not a good idea

we can say thats the case in terms of the symbols we use, sure, but beyond that no notion of > or <

we can say x + -y is the same as x - y

[waxen musk]

im gonna be honest, ive been saying that some time ago

[twilit jetty]

but thats about it, x - y doesnt have to be smaller than x

you could have x + --5 and x - -5

[fathom onyx]

Well, "adding a negative number" isn't subtraction; a more appropriate phrasing would be
"adding a negative number is equivalent to subracting the positive number (that the negative number is the negative of)"

[twilit jetty]

a more useful idea in general is that we dont attribute much to the output of an action, at least for now

[fathom onyx]

(This is not the same as saying that one thing IS the other; caution is needed there)

[sly cape]

i think this is something that scientist would be interested in

and what they need

[sly cape]

wrong. "the process or skill of taking one number or amount away from another."

[twilit jetty]

oval, I have to break it to you

the mathematical definition of addition and subtraction doesnt align with the common real world use of addition and subtraction

but as mathematics becomes more commonly taught,

the mathematical definition is then a lot more common

you know back then people couldnt even think of negative numbers, because it would mean to have less than nothing

0 as a concept is relatively new in human history

[fathom onyx]

The "common" definition there doesn't by default take negative numbers as elements that can be used

[sly cape]

but people knew what "owing" meant

[twilit jetty]

its up there with the printing press and the car in "surprisingly recent inventions"

[twilit jetty]

yes, you are missing something, but as a concept?

you owe sheep, you owe land, you dont owe numbers

what would it mean to even owe to a number? is 5 going to break down your house?

[sly cape]

you owe 2 sheep

[twilit jetty]

doesnt mean you "have -2 sheep"

[sly cape]

which - translate to not have

[twilit jetty]

it just means you need 2 sheep

[fathom onyx]

Taking "owing" something as literally a negative of "owning" something is a relatively new concept

[sly cape]

youre on minus balance

just like a bank account

[fathom onyx]

Credit/debit book-balancing doesn't even rely on negative numbers, though

Again, it bends over backwards to avoid them

[twilit jetty]

you know people used to attempt to solve ax^2 + bx + c = 0

but without negative numbers,

they came up with like 17 different variants of the equations, all only using positive numbers

[fathom onyx]

-# (I have some, albeit minimal, experience with this)

[sly cape]

when?

[twilit jetty]

so instead of solving x^2 - x + 4 = 0,

theyd solve x^2 + 4 = x

and negative numbers would be removed out of it

[twilit jetty]

I dont exactly remember my math history, but its around the medieval ages or the enlightenment

[fathom onyx]

Literally up until the 16th century was what mtt saying the normal approach

[twilit jetty]

it predates the quadratic formula

[sly cape]

so negative numbers didnt exist?

[twilit jetty]

they existed to no one, because they couldnt conceive of them

[fathom onyx]

That's literally what he's been trying to tell you

[twilit jetty]

up until now, where we can define negative numbers

and in doing so, we also must redefine addition and subtraction

addition means to mix, subtraction means to negate the second number then mix

--4 = 4

[waxen musk]

they didnt even have symbols they would literally say "the area of a square plus 4 is the side of the square"

[twilit jetty]

and -0 = 0

[sly cape]

So you said that people couldnt for example remove 1 sheep from 2 sheep?

[twilit jetty]

youd just get 1 sheep oval, say that slightly differently

they cant remove 2 sheep from 1 sheep

[fathom onyx]

Heck, the fokken EQUALs sign wasn't even commonplace until the 1500s

[twilit jetty]

because you only have the 1 sheep

consider this, the idea behind negative numbers is common, but the idea of a negative number is recent

[burnt flame]

this is still going

[twilit jetty]

if you had 5 apples, and you needed 7,

[sly cape]

"=" replaced equals to

[twilit jetty]

youd think "Im going to take 5 apples and I still need 2 more"

youre not going to think "I currently have negative 2 apples"

[fathom onyx]

and the reason it even exists at all was because one guy decided to express that two things were equal by representing them as two incredibly long lines that were of equal length

[twilit jetty]

so in short,

mathematics didnt get here through arbitrary rules

[fathom onyx]

Like, this was from 1557

[sly cape]

no, you'd have 5 apples

[twilit jetty]

oh sorry, let me elaborate

if you had 5 apples, and you needed to give someone 7 apples,

youd think "Im going to give 5 apples and I still need 2 more"

that was a major typo, I dont know how that got mixed up

[stone ivy]

@sly cape bro what is this thread about at this point?

[sly cape]

that doesnt make sense

[twilit jetty]

oval doesnt think 5 + -4 should be called addition because you end up subtracting to get a smaller result

[sly cape]

Some people can't accept my theory

Or well the truth

[twilit jetty]

"some people" being the math community

[waxen musk]

what is your theory

[fathom onyx]

Your theory's demonstrably wrong, is what people are trying to get at

[stone ivy]

What is your theory?

[fathom onyx]

Or at the least, subpar

[twilit jetty]

Id say its inefficient

[sly cape]

Not a theory

[twilit jetty]

its more suitable for modern math today to change + and - to what they are

[waxen musk]

what is this thing, then

[sly cape]

But a correct way to express that

[fathom onyx]

A game the-

[sly cape]

I'm probably not only one who thinks that

[stone ivy]

bro are you guys discussing history or philosophy or somethin'? Cuz this ain't any maths.

[waxen musk]

like, what concretely are you saying, im genuinely lost atp

[twilit jetty]

to date, you are the only person who thinks that we need to make addition and subtraction great again

[fathom onyx]

Metamathematics blurs that line very quickly, so don't get too cocky with that

[sly cape]

@stone ivy I just wanted to know the difference between multiplying (-2) or without brackets

[twilit jetty]

no you dont

you also think 5 + -4 is subtraction

[sly cape]

I gave example at the beginning.

[twilit jetty]

you said -x^2 should be viewed as (-x)^2

[sly cape]

Cause you will end up with 1 instead of 5?

[twilit jetty]

so -5^2 should be -5 * -5

[twilit jetty]

see here the idea at play

[sly cape]

Subtracted.

[twilit jetty]

yep

addition isnt being real there

[sly cape]

Yea so now you agree?

[twilit jetty]

even though theres a + sign

[sly cape]

do you mean this?

[twilit jetty]

bro thats a common thing people do where they repeat your point to make sure they got it right

Im repeating it to make sure I got what you said right, doesnt mean I agree with it

[stone ivy]

What is metamathematics?

that's a hard word to pronounce.

[twilit jetty]

meta-mathematics

you can pronounce it like that

[sly cape]

So this is a subtraction.

5 + -4

[waxen musk]

math about math itself, but this isnt super relevant here

[sly cape]

@twilit jetty

[twilit jetty]

we dont call it that

we call it adding a negative number

which ends up as subtracting a positive number

thats because you used a + sign, that is all

[fathom onyx]

It's what happens when Mark Zuckerburg decides he wants to fu-
It's the study of mathematics itself, using mathematical methods

[twilit jetty]

5 add -4 means 5 + -4

[sly cape]

It's like -4*4, the positive (plus) just evaporates

[twilit jetty]

theres ideas in there I think about ZFC, the minimum amount of rules you need to build most of mathematics

[twilit jetty]

so if we were to do -2 + x,

do we really have to use two different kinds of names?

[stone ivy]

I know but pronouncing it in one go makes one's speech become something. I can't describe what it becomes but surely you can feel what I'm saying.

[twilit jetty]

one for when -2 + x gets bigger, one for when -2 + x gets smaller?

[twilit jetty]

yea, try it slow, try it fast, thats all
its a slur seeing all of those E and A together

[sly cape]

Yes.

[twilit jetty]

and what are we going to call the + sign then?

[sly cape]

As it is more precise.

[sly cape]

Addition, but only with a positive number.

[twilit jetty]

no really

how do you write -2 + x into words then

and remember, this whole time in history

our progress has been in making math easier to read and speak

[sly cape]

sum of -2 and x

[twilit jetty]

doesnt sum mean add

youre going to just defer to the word sum now?

[sly cape]

yes, but x isn't negative

[twilit jetty]

x can be negative oval

[sly cape]

so -2 will just go greater

[sly cape]

sure if it was -x

[twilit jetty]

x can be -5 you know

doesnt have to have a - sign before it

the letter x doesnt only stand in for positive numbers

[fathom onyx]

x just stands for "a number" here at this point

Without any concern for whether it is positive, negative or zero

[sly cape]

Yea so it an addition up until the unknown is known

[fathom onyx]

(I think another thing that has to be explained is that zero is specifically neither positive or negative)

[twilit jetty]

repeat that sentence to make more sense too

if we dont know whether x is positive or negative,

what would you call -2 + x, in words?

write it out in full for me

[fathom onyx]

And bear in mind you can't use "sum", because that defaults to addition, and as per your words this can't always be an addition

[sly cape]

We can call this -2 + x an addition,

[twilit jetty]

the full thing please

[sly cape]

What fulll thing?

[twilit jetty]

if x is negative, you couldnt call -2 + x an addition because then you end up subtracting

if x is negative, what would -2 + x be called then instead

[fathom onyx]

You're answering the question

if we dont know whether x is positive or negative,
what would you call -2 + x, in words?
as a full sentence

Meaning you need the "if..." part as well

[sly cape]

Basically this is undefinied

Until x is known

[twilit jetty]

oval, that only works in elementary school

[fathom onyx]

Okay, there's another concept you seem to be confused with

"undefined" has a definition, ironic though this sounds

[twilit jetty]

as we get into higher math, we do need x to be general like this

we need a name

a description

what are we going to call -2 + x?

[sly cape]

Well I can call this adding and then changing the unkown to a numer which then results into subtracting (if so)

[twilit jetty]

oval, I hope you understand,

thats a long-ass name

[fathom onyx]

But IF WE DO NOT KNOW WHAT x IS, this is useless

[twilit jetty]

and thats why we just use the word "plus"

thats the reason why addition does what it does

we consider addition and plus to be a shorthand for +

[twilit jetty]

not only because of this,

[sly cape]

undefined number

[fathom onyx]

@sly cape

Just because you don't know what this is equal to, doesn't mean you can call this "undefined"

[sly cape]

Or Unfinished equation

[fathom onyx]

That's not what the word means

You can't call it that either

Because that implies this is TO BE an equation

There's nothing here that suggests that it SHOULD be one

[sly cape]

-2 + x this tell us what?

Nothing

if we dont know the x

[twilit jetty]

this tells us an expression that needs to do the operation of addition on -2 and x

oval,

-2 + x actually does mean something

it has a picture, for example

[fathom onyx]

This tells us we have SOME QUANTITY x, and we're +ing the number -2 to it

[sly cape]

not in a sense of solving it

[twilit jetty]

which looks like this

[twilit jetty]

that sounds like eugenics oval

[fathom onyx]

You're getting worked up with the word "solve " here, as well

[twilit jetty]

math only exists to be solved?

[sly cape]

yeah but graphs dont really matter in maths

[twilit jetty]

you say that kind of talk with anything else and youre going to look insane

but for math, everything is only to be solved?

I just want a noun man

something to call -2 + x

and until then, we're just going to call it "-2 plus x"

because its short and its simple

[waxen musk]

hmm this is moreso all the points (x,y) which satisfy y = -2 + x, because we need the statement here

[sly cape]

Sure because you'd like to know what paycheck you got? Oh they will say x-1000 (example)

[brittle grotto]

wow. how has such a long conversation sprung from a minor notational question

[twilit jetty]

well yea oval

youve never done your taxes before?

social security?

how are those written?

[sly cape]

Are you making me dumb?

[twilit jetty]

(gross income) * something, thats for sure

theres an expression for you

[sly cape]

But youre now saying that math doesnt need to be solved

[twilit jetty]

you went further

[sly cape]

okay then you won't know the answer

[twilit jetty]

now youre saying theres no point in making any expressions

[twilit jetty]

here

if the tax is 8.75% in your state, that means you do (current price) * 1.0875 to get how much it costs after tax

theres purpose in formulas

Id like to know how much I need to pay for something, and thats (current price) * 1.0875

how do we use it? we can use it for more than just one price, for example 19.99 * 1.0875

we can use it for any price in the region we are in

[twilit jetty]

if they say this, they mean "we had to take away $1000"

what you lose in being specific, you gain in being general

[sly cape]

Okay but you said that some mathematics equation should be left out without a solution or something like that

[twilit jetty]

this is the nature of math, it says how things can be like in general

[twilit jetty]

yep, because (current price) * 1.0875 fundamentally isnt a solution to you

if you wanted to, for example find how much $99.99 costs after tax,

and I told you to do that

[sly cape]

And so isn't just an x a solution

[twilit jetty]

oval listen to me

[twilit jetty]

you still have to bring a calculator to do this

(current price) * 1.0875 by itself isnt a solution to a specific problem

its only a solution to a general problem of "how do I calculate the price after tax?"

[sly cape]

exactly

[twilit jetty]

if I had $99.99 * 1.0875, that can answer "how do I calculate the cost of a $99.99 product after tax?"

but it cant answer "now what about this $74.99 product?"

(current price) * 1.0875 and $99.99 * 1.0875 are only solutions to their kinds of problems

one for the general, one for the specific

and youre thinking "only the specific ones matter"

[twilit jetty]

for example, here

-2 + 5, but never -2 + x

[sly cape]

THere's a difference between knowing how to calculate and how to do it

[fathom onyx]

"how can I hammer a variety of nails into this wall?"
"fuxk me idk, hammers are undefined"

This is not far off from how your train of logic reads

Related question - you do know the difference between an equation and an expression, right?

[twilit jetty]

those words dont mean what you think they mean, please elaborate

[sly cape]

Sure im not that dumb

[sly cape]

But what's the point of telling this?

[twilit jetty]

put it this way

we have a description for -2 + 5

"negative two plus five"

"adding negative two and five"

these are examples

[fathom onyx]

The POINT is that, "current price" is our unknown variable

[twilit jetty]

but lets say we need to represent adding -2 to something in general

now naturally youre not going to be happy with the word adding...

because that something could be my debt, which is negative

so what would our description of -2 + x be?

[sly cape]

Unsolvable subject

[twilit jetty]

now heres something I dont think youre familiar with

we in fact can do things with -2 + x

its true that we do not know what -2 + x's value ever is

given we dont know x's value

but that doesnt stop us from doing math on -2 + x itself

[sly cape]

oh i know where you going

[twilit jetty]

so if we need to do math on -2 + x itself,

we need a noun for it

and is "unsolvable subject" really going to tell someone what youre seeing on the screen?

[sly cape]

youre just talking about basic algebraic equation?

[twilit jetty]

you can afford more words than that

[stone ivy]

This thread is truly getting ridiculous.

[twilit jetty]

I didnt use an = sign

so no, Im not

for example, the slope of -2 + x is 1

thats an example that doesnt use an equation

[sly cape]

i know right, we also talked about pemdas and bodmas and if divison or multipication went first

[fathom onyx]

(which is why I'd asked whether you knew the difference between "equation" and "expression", because you keep using one term to mean the other)

[twilit jetty]

(the guy in question thought multiplication and division could be done in any order, with one of them first, etc., even after showing they knew the correct way)

[sly cape]

but you guys misinformed me in the first place

[twilit jetty]

you misconstrued us

I dont believe youre the perfect arbiter of the english language

[sly cape]

you said that those were two different things

[twilit jetty]

its possible that, just maybe, you misread something out of the very complex idea on display here?

[twilit jetty]

as different as color and colour, cmon man

different names for the same things

[sly cape]

not really

[sly cape]

nope

the order was different

[fathom onyx]

Fuxk me, "words have definitions" should not have to be a concept that needs explaining

But it's getting to that point

[twilit jetty]

you do know what BODMAS means right

it means B, O, DM, AS

[sly cape]

why would be everything be in order but division and multiplication

[twilit jetty]

it doesnt mean B then O then D then M then A then S

[twilit jetty]

because its literally a turn of phrase, it doesnt need a meaning

[sly cape]

Yea and they flipped

[twilit jetty]

yep

[sly cape]

one had DM other MD

[twilit jetty]

and what are you going to do about it?

we cant do anything about it

[sly cape]

yeah so you misinformed me that those were different things

[sly cape]

Yeah but you brought it up

[twilit jetty]

those were different names oval

yea because you mentioned them first when I entered the conversation

[sly cape]

With the same order with those changed

[twilit jetty]

you mentioned both BODMAS and PEMDAS in the same message

[fathom onyx]

@sly cape No he didn't misinform you; you didn't read what he said

[twilit jetty]

an independent third party here looking over the messages and confirming that, yes, theres more meaning to the differences than just the word "different"

you know not everything can fit into one message, they need elaboration

[slate ferry]

3(-2) looks a lot better than 3 -2 which could be interperted incorrectly

[sly cape]

well the whole point was to talk about exponents and multiplication, not the correct order of doing them

[twilit jetty]

and the concept I elaborated on is exactly the same concept I am telling you now

[fathom onyx]

But since you've been confusing + and -, he's had to take it into a more elementary situation to explain things before you even consider the order of operations

[twilit jetty]

I think you have larger fish to fry than just that

theres a distinct lack of care here, you dont care about any of this

you just think youre right without ever hearing the other side out

[sly cape]

we'll not my fault for different meaning

[fathom onyx]

So don't think he's diverting the conversation; you're missing, and more importantly displaying a lack of, a crucial understanding

[twilit jetty]

it is your fault when I give you the meanings and you dont read them

its a fault of a lack of care, that you just want this one question answered and not realizing how far up you need to climb

this is a flat earther asking "how do I explain the motion of the moon?" then being surprised when we have to explain the heliocentric model

[sly cape]

yea but we were talking primarly about -x^2 and -(x)^2

[waxen musk]

@sly cape what is your question at this point? is it still on the 3(-2) notation?

[twilit jetty]

please understand: you are stating a dangerous precedent

we can show you how mathematics commonly answers these questions, so that you can learn their language

we cant fix the typos in the words we see, we cant remove the silent letters

but we can tell you how it works so you can get used to it

you dont have to agree, I often times dont, but you have to use the words

[fathom onyx]

But if you're going to misunderstand - and misuse - their language from the outset, you're going to keep slipping on banana peel after banana peel

[sly cape]

Yeah but like my goal was to prove that I was right with the subtraction and addition. Everyone can express and feel education to their own discretion. There´s no final answer to it. Just like what is the biggest number ?

[slate ferry]

great! no difference whatsoever! It's just helpful in some situations like functions! which you are yet to take.

[sly cape]

Well, thats not

[sly cape]

I´m trying to, but you all turned it into confusing, complex scenarios

[twilit jetty]

as if:

[slate ferry]

again, i must state, there is a language barrier between oval and us!

maybe this is jut a big misunderstnading

[twilit jetty]

as they stand, you do not have enough mental material to find the error in your own points

just like the flat earther here

[sly cape]

we already explained it

[twilit jetty]

that is why we are giving you more material to show you that theres a damn good reason we do things this way and not the other way

I couldnt even finish telling you that in both examples

[waxen musk]

so, you do not have any further questions at this point?

[twilit jetty]

the addition and the ^ thing

if you do not want to be convinced, there is nothing we can do to help you

[waxen musk]

or you mean that you already explained your question?

[sly cape]

probably I Q difference but idk

[twilit jetty]

times up for me, I gtg

[sly cape]

Well not quite

[waxen musk]

please do not be rude to the helpers

[sly cape]

There are many factors to this

[slate ferry]

wait do you mean 💀

[sly cape]

Well i didnt say i had higher

i have lower

[waxen musk]

oh ok

[slate ferry]

yeah thats what i thought

[sly cape]

Really?

[slate ferry]

ok listen dear, do you have any more concerns

[waxen musk]

so, lets adjust to get back on the topic of your question

[sly cape]

I stayed up til 3 am for this..

And we're just gonna leave it unsolved

Oh wow he left..

[slate ferry]

no!

we'\re here

hellooo

[waxen musk]

are you still having issues with the difference between (-x)^2 and -(x)^2

[sly cape]

Yes

[brittle grotto]

ok can I just put in my two cents

math notation is meant to be as clear as possible

generally, it's not worth obsessing over some divinely correct interpretation of an expression

[waxen musk]

so, concretely, when we say
(-x)^2, by definition, we mean (-x)^2 = (-x)*(-x)
-(x)^2, by definition, we mean -(x)^2 = -(x)*(x)
does this distinction make sense to you @sly cape ?

[sly cape]

But argumentation, discussing is a crucial part generally speaking.

[olive matrix]

hey so just a reminder to everyone here that you are always free to leave this conversation at any point if it's making you upset or angry

[slate ferry]

perhaps focus a bit with @waxen musk

[sly cape]

Yeah exactly the word interpretation

The whole discussion was (maybe not the beginning cause it was about pedmas )

[brittle grotto]

here's the thing

we generally read -x^2 as equivalent to -(x)^2

and this is a well-established convention

[sly cape]

no, like x^2 and -(x)^2and (-x)^2

[brittle grotto]

so I guess... my question is... are you expressing a personal distaste of this convention?

[sly cape]

okay so

-x^2 is -x * -x

[brittle grotto]

welll... I would not write it like that

it may be more clear to write it like (-x)*(-x)

[waxen musk]

not according to the standard grammar in math

[sly cape]

I think mtt even said that

nvm only one -x

[waxen musk]

yes, this grammar is entirely arbitrary, but we keep this standard to make it clear (and also we are a bit lazy)

[brittle grotto]

the righthand expression you wrote might be seen as a little unclear, oval

[sly cape]

which

[waxen musk]

in fact, literally everything should have parentheses around it, but we omit them because we are lazy

[brittle grotto]

#help-49 message

[sly cape]

Okay so lets start from beginning

[waxen musk]

but we need a rule to do this, or else its ambiguous

[sly cape]

-x^2 = -x * x

[waxen musk]

yes

[sly cape]

and then -(x)^2

[waxen musk]

we use pemdas to omit the parentheses here, we have that -x^2 = -(x)^2

[sly cape]

really its the same answer?

[waxen musk]

yes

in both cases, we want to do ^2 to the x first

[sly cape]

so its -(x) * -(x)

[waxen musk]

no, remember what we said about -x^2 here

you brought a stray - sign

all were saying with the parentheses in -(x)^2 is that we want to do ^2 to x first, we are not doing - to x first

does that make sense to you?

[sly cape]

oh yeah so x * x and we bring the minus?

[waxen musk]

yeah

now what about (-x)^2

[sly cape]

and with (-x)^2 do we copy twice the minus?

[waxen musk]

yup

[sly cape]

thats soo easy

[waxen musk]

so, now you are absolutely clear on the difference between (-x)^2 and -(x)^2 and -x^2?

[sly cape]

-x^2 = -x * x
-(x^2) = -x * x
(-x)^2 = -x * -x

[sly cape]

check below

[waxen musk]

good

now, do you have any further questions? or does everything make sense to you

[sly cape]

i think its okayyy

but idk if i should close

[waxen musk]

well, if you have points of uncertainty, you should utilize my help

[sly cape]

also i have one question

[waxen musk]

but otherwise, if you dont want to, you can close

yeah, go for it

[sly cape]

do you know SYSTEMS OF EQUATIONS?

[waxen musk]

yeah

[sly cape]

How to do this using the substitution method? We don't have a single algebraic letter..

[waxen musk]

so, this is telling us to solve for when both equations are true
take one equation, doesnt matter

lets start with the 2x+3y=8

solve for one of the variables

lets say x

how do you rewrite 2x+3y=8, but as x=...

[waxen musk]

so first, does it make sense what im asking here? second, is it clear how you would go about just this part?

[sly cape]

3x = 8 -3y

[waxen musk]

2x = 8 - 3y

[sly cape]

ik that but i want to have 1x

sorry

2x

[waxen musk]

its okay

[halcyon vale]

how do you turn 2x into 1x?

[waxen musk]

i can divide both sides by anything but 0

what should i divide 2x by to make it simply x

[sly cape]

maybe divide the other side with 2x too

[waxen musk]

that would just give us 1

[halcyon vale]

but if you divide both sides by 2x you'll be left with 1, not 1x

[sly cape]

(8-3y)/2x

[waxen musk]

we still want the x here

but youre close

[sly cape]

but with 2

not 2x

[waxen musk]

mhm

[sly cape]

(8-3y)/2

[waxen musk]

yep

[sly cape]

thats easy

[waxen musk]

we can simplify this, itll make it easier

how do i simplify (8 - 3y)/2

[sly cape]

it will be

4-3y

[waxen musk]

you got the 4 part right, but you lost the /2 on the 3 part

you have to divide both numbers by 2

[sly cape]

yeah which is 4-3y/1

= 4-3y

[halcyon vale]

you should be dividing by 2, not 1

[waxen musk]

now, youll be saying 3/2 = 3/1 if you do that

[halcyon vale]

what is your thought process behind dividing 3y by 1?

[slate ferry]

brackets here are important! you see, its asking you to divide the whole thing by 2, n ot just 8 or not just 3y... you need to divide the both of them by 2 which is indicated by the brackets

[sly cape]

$\frac{8 - 3y}{2}$

[grand pond]

TrulyOval

[waxen musk]

yes

[slate ferry]

ahaaa

[waxen musk]

now how do we continue from here

[sly cape]

its easy to divide 8 and 2

[waxen musk]

good

[sly cape]

and 2 : 2 is 1

so it will just be 4-3y

[waxen musk]

what do you mean 2:2 is 1 here?

[sly cape]

divided

2 and 2

[waxen musk]

thats a ratio, which is slightly different than a fraction first of all

[sly cape]

well thats how i mark division

[waxen musk]

but yes, 2/2 = 1, but we actually have 3/2 here

how did you arrive at 2:2?

[sly cape]

wait

i have an idea

[waxen musk]

hm?

[sly cape]

$2(8-3y)$

[grand pond]

TrulyOval

[waxen musk]

we cannot say x = 2(8-3y)

[sly cape]

why? i eliminated denominator

[slate ferry]

by... putting it in the numerator? well that's not justified.

[waxen musk]

because thats exactly saying $\frac{x}{2}=8-3y$ and $\frac{x}{2}\neq 2x$

[sly cape]

well multiplied

[grand pond]

Cycadellic

[waxen musk]

dividng 2 was the correct step here

we now need to simplify $x=\frac{8+3y}{2}$

[grand pond]

Cycadellic

[sly cape]

1/2 * 2 = 1 so its solved

[waxen musk]

where is this *2 coming from?

[sly cape]

from denominator

[waxen musk]

what do you mean from denominator?

[halcyon vale]

what if we just dont simplify it? x gets multiplied by 4 in the second equation so theres no need to simplify this expression

[waxen musk]

yes, but how did that translate to *2?

[waxen musk]

i want oval to simplify this so they understand

[sly cape]

yeah

[waxen musk]

i see them bring a *2, so thats a clear point of confusion which must be hammered out

[sly cape]

i get it

now

[waxen musk]

so what do we have?

x=...?

[waxen musk]

so, we have this rule

$$\frac{a+b}{c}=\frac{a}{c}+\frac{b}{c}$$ for any possible $a,b,c$ except $c\neq0$ because we cant divide by 0

[halcyon vale]

\frac{\left(a+b\right)}{c}=\frac{a}{c}+\frac{b}{c}

[grand pond]

Cycadellic

[waxen musk]

oh woops

[sly cape]

right

[waxen musk]

its (8-3y)/2 lol not +

but yes, the rule still applies

so, $$x=\frac{8-3y}{2}$$

[grand pond]

Cycadellic

[waxen musk]

where to go from here

[sly cape]

\frac{4}{1} + \frac{3y}{2}

$\frac{4}{1} + \frac{3y}{2}$

[grand pond]

TrulyOval

[waxen musk]

correct

[sly cape]

yayayayay

[waxen musk]

do -

i accidentally said +

[slate ferry]

https://tenor.com/view/have-a-great-day-gif-13578415868193855261

[waxen musk]

its actually -

[sly cape]

$\frac{4}{1} - \frac{3y}{2}$

[waxen musk]

great

now for the substitution

[grand pond]

TrulyOval

[stone ivy]

guys just stop. get some help.

[waxen musk]

$$x=4-\frac{3}{2}y$$

[grand pond]

Cycadellic

[waxen musk]

we substitute this into $4x+5y=15$

[grand pond]

Cycadellic

[waxen musk]

do you know how?

[sly cape]

ik

[scenic wyvern]

if you are not helping and can't stand this conversation, you may ignore this thread for the time being, because this is a different question now.

[slate ferry]

big brackets moment incoming!!!!!!!!!

[sly cape]

$4\left(\frac{4}{1} + \frac{3y}{2}\right) + 5y = 15$

[grand pond]

TrulyOval

[slate ferry]

YEAH

GOODJOB

[waxen musk]

now, do you know what to do from here?

[stone ivy]

rude but facts

[sly cape]

yea yea

$\frac{16}{1} + \frac{12y}{2} + 5y = 15$

[grand pond]

TrulyOval

[waxen musk]

good, now, what do i do about the y?

[slate ferry]

YES! GO BRACKETS WORK GO

[stone ivy]

$y = \frac{-1}{11}$

[slate ferry]

?

!nosols

[midnight plank]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[slate ferry]

wait its wrong lmao

[waxen musk]

also, not quite

[slate ferry]

still

[stone ivy]

Oh I see the mistake my bad

[sly cape]

16 + 6y + 5y = 15

[slate ferry]

ahaaaaa

[waxen musk]

now, how do i get a single y here

[slate ferry]

what is this person doing

[waxen musk]

idk

[sly cape]

16 - 15 = -11y

[waxen musk]

yes

lol

[grand pond]

fort craft 🇵🇸

[scenic wyvern]

!nosols

[midnight plank]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[scenic wyvern]

let the helpee try it themselves

[waxen musk]

almost there now

[stone ivy]

What does !nosols mean? No solutions?

[waxen musk]

whats 16-15

[sly cape]

-11y = 1

[slate ferry]

dont give answers to the person we're trying to help.

[sly cape]

yep 1

[scenic wyvern]

@stone ivy

[waxen musk]

now we finally solve for y

[stone ivy]

@scenic wyvern@slate ferry sure. I won't.

[slate ferry]

GO OVAL GO

[slate ferry]

thank you fam./

[sly cape]

so to eliminate i can just multiply both sides with -1