well the problem either doesn't make sense or is poorly written
#help-0
spare moss
Yeap
spare moss
The one i encircled is the only thing im confused
spare moss
So here's the list of questions that im confused can't answer lol: K or M only, K or C but not M, K and C only, M and C but not K, Exactly 1 of the 3,Exactly 2 of the 3, Atleast 1 of the 3, Atleast 2 of the 3, None of the 3
My wifi got out
Sorry
So sorry
@vale wigeon
End
!end
.close
lone heartBOT
lone heartBOT
Available help channel!
thick lynx
We have that U_total = U_1 = U_2 = ... in a parallel circuit, but why is this, even though the resistors could be stronger or weaker on one end?
languid bolt
i will translate one second
channel taken
thick lynx
i will translate one second
Please send this in an unoccupied channel, for example #help-2
remote yew
im sorry
thick lynx
np
I will repost my original question to get it down again:
We have that V_total = V_1 = V_2 = ... in a parallel circuit, but why is this, even though the resistors could be stronger or weaker on one end?
And the voltage changes after it goes through a resistor
lone heartBOT
@thick lynx Has your question been resolved?
thick lynx
<@&286206848099549185>
lone heartBOT
@thick lynx Has your question been resolved?
fluid otter
i need help to get my channel
cobalt needle
I was confused at the question which is “a cuboid with no top uses 54m^2 of metal. What is the maximum volume of the cuboid” and in the answer video they presume two of the faces have equal width and height as shown above
cobalt needle
Why can you presume this?
last ether
Because it's a cuboid
A cuboid is a rectangular prism with some square cross section
Actually wait
,w cuboid
ocean sealBOT
cobalt needle
A cuboid is a rectangular prism with some square cross section
Oh thanks my bad I thought it just had to have all faces being quadrilaterals
last ether
Well hold on
I might've confused it with a square rectangular prism
I guess it's to simplify it
But like, things typically get optimized with squares
Maybe they just did it to make it simple
last ether
I mean, unless they explicitly stated it had square sides, no
cobalt needle
Nah nemesis thanks thing
Nvm that’s stem discord
Sure please can you close it as I can’t remember and I’ll presume it was an error in the video
last ether
.close
lone heartBOT
lone heartBOT
Available help channel!
vague iris
I'm not familiar with this format. Can u guys please help me?
lone heartBOT
I'm not familiar with this format. Can u guys please help me?
@vague iris Has your question been resolved?
pseudo pine
Hello
balmy grail
Are you asking is magnitude equal to absolute value?
lone heartBOT
ruby current
you can also see via |-a| = |-1| |a| = |a|
lone heartBOT
Available help channel!
alpine sable
Sos
alpine sable
I did it this way but is wrong 👇
How so? First 1/6 is for selecting the 6, 5/6 is for any other than 6
1/6 is to repeat the value in teg previous 5/6
And 4/6 for any other random value not selected 👇
First two 1/6 is for selecting 6 twice
5/6 is for selecting any other value other than 6
4/6 is for selecting any other value other than 6 and the previous value 👇
So how is my method wrong
lone heartBOT
@alpine sable Has your question been resolved?
slow marsh
mighty cliff
lone heartBOT
lone heartBOT
@mighty cliff Has your question been resolved?
mighty cliff
.close
modest sleet
i need to calculate this
lone heartBOT
i need to calculate this
modest sleet
wind cloak
$\sum_{k = 1}^n k!k$
ocean sealBOT
jan Nejon
ocean sealBOT
jan Nejon
modest sleet
thx
wind cloak
$\sum_{k = 1}^n k!(k + 1) - k!$
ocean sealBOT
jan Nejon
ocean sealBOT
jan Nejon
wind cloak
It telescopes
slow marsh
lone heartBOT
@alpine sable Has your question been resolved?
lone heartBOT
@alpine sable Has your question been resolved?
carmine reef
Replace u_n and u_n+1 with the formulas for them
lone heartBOT
@alpine sable Has your question been resolved?
low quest
how do i solve for this problem?
lone heartBOT
how do i solve for this problem?
odd seal
$\mathbb{F}_{\text{un}}$
ocean sealBOT
sakka ismail
low quest
.close
burnt ivy
what are they doing here to put wi in terms of h?
lone heartBOT
what are they doing here to put wi in terms of h?
burnt ivy
lone heartBOT
@burnt ivy Has your question been resolved?
burnt ivy
<@&286206848099549185>
lone heartBOT
@burnt ivy Has your question been resolved?
burnt ivy
.close
golden ridge
if (an) is real sequence satisfying 0 < an < a(2n) + a(2n+1), determine the nature of the infinite series of an
golden ridge
please'
golden ridge
can you say anything here
wdym
remote heron
but it seems like this could be divergent or convergent
the harmonic sequence satisfies this right 
no
im just bein silly
golden ridge
the harmonic sequence satisfies this right <:thonk:406575732563902485>
nope
HELP
🆘
@here
pleaseee
remote heron
😭
golden ridge
thank you bro @remote heron
remote heron
im sorry i just am not sure
golden ridge
nah it is fine man nevermind lol
glacial patrol
vapid shuttle
if (an) is real sequence satisfying 0 < an < a(2n) + a(2n+1), determine the natu...
this is true of any increasing sequence no?
if an increasing then certainly a2n > an and same for a(2n+1)>an
glacial patrol
yeah
vapid shuttle
and then even more certainly their sum is larger
so like
it doesn't necessarly converge?
lone heartBOT
@golden ridge Has your question been resolved?
left zealot
how do I do this
left zealot
<@&286206848099549185>
sour verge
The line segment CD is perpendicular to the line for which you already have the equation.
What is the slope of a line perpendicular to a line of slope $a?$
ocean sealBOT
Azyrashacorki
lone heartBOT
@left zealot Has your question been resolved?
left zealot
What is the slope of a line perpendicular to a line of slope $a?$
y = mx+b
sour verge
A line perpendicular to a slope of $a$ has a slope of $\frac{-1}{a}$
ocean sealBOT
Azyrashacorki
left zealot
**Azyrashacorki**
it always has this?
sour verge
Yes
If you have a line with a slope m
Then the slope of a line perpendicular to it is always -1/m
So now in your problem, you can find the slope of the perpendicular line using this trick
left zealot
Then the slope of a line perpendicular to it is always -1/m
there's no m tho, it's D, E and F
sour verge
I thought you needed help with the circled problem lol
If DEF is 90 degrees
Then the lines going through DE and the line through EF are perpendicular
So their slopes agree with m = -1/m
left zealot
I thought you needed help with the circled problem lol
oh mbb
I mixed up the questions
I only need help with #1
sour verge
Oh ok
left zealot
so how do I start
left zealot
**Azyrashacorki**
yes
sour verge
And you want the equation of another line that is perpendicular to it and goes through the point C
As per what I mentionned earlier with perpendicular slopes, what would be the slope of the perpendicular line?
left zealot
As per what I mentionned earlier with perpendicular slopes, what would be the sl...
-2
sour verge
Yes
So now you know the perpendicular line will havethe form y = -2x + b
You can now just plug in the point C in there for x and y and solve for b!
lone heartBOT
@left zealot Has your question been resolved?
meager linden
lone heartBOT
molten pivot
divide the numerator and denominator by the gcd
so like what number goes into both 4 and 32
the biggest such number
queen juniper
gcd?
greatest common denominator
what can you divide both by to simplify the equation
meager linden
why have the helper role?
glacial patrol
I dropped out of math school
Take off the helper role bruv
meager linden
greatest common denominator
what can you divide both by to simplify the equation
thats what confuses me
how do you find the gcd
queen juniper
try looking at the smallest number first
like 4/32
what goes into 4 evenly that can also go into 32
meager linden
uh
queen juniper
sorry didnt mean to put you on the spot just giving an example 💀 :3
meager linden
you good
meager linden
try looking at the smallest number first
like 4/32
what goes into 4 evenly th...
🤷
wdym "what goes into 4 evenly"
meager linden
yeah
queen juniper
10/5 is though
meager linden
mhm
queen juniper
oh wait are you asking what i meant by evenly or how to do that
meager linden
rn im just confused how to get the gcd
queen juniper
try looking at the smallest number first
like 4/32
what goes into 4 evenly th...
this
meager linden
i dont get this part - what goes into 4 evenly that can also go into 32
queen juniper
i dont get this part - what goes into 4 evenly that can also go into 32
bad phrasing on my part sorry
like what is the highest number you can divide both by that will still be a whole number
meager linden
2?
queen juniper
so lets start with 2
4/2 = 2
32/2 = 16
now we have 2/16
which still isnt simplified but you can do the same thing to continue trying to find the gcd
meager linden
1/8?
queen juniper
yup n thats how 4/32 -> 1/8
queen juniper
start with the same thing
what is the highest number you can divide both 9 and 25 evenly
meager linden
idk
queen juniper
do you know the factors of 9(?)
meager linden
1 3 9
queen juniper
so those are some starting numbers you can try because you know those 3 will be able to divide evenly into 9
then you try and see if they do the same for 25
meager linden
yes
queen juniper
thats as far as that can simplify
meager linden
alr ty
queen juniper
np :3
lone heartBOT
@meager linden Has your question been resolved?
sweet nymph
help
vapid shuttle
use rules of logarithims for log(a)+log(b)
sweet nymph
i got log(x(x - 1) = log 10
vapid shuttle
yea
sour verge
Take the exponential function on both sides.
chrome salmon
Hi
sweet nymph
x^2 - x = 10
sour verge
Now solve using quadratic and make sure your answer(s) is(are) consistent with the original equation
i.e. x>1
sour verge
Since you have log(x-1)
alpine sable
\
alpine sable
im not sure what that person did in that step
the first image is the solution to the problem
but im not sure what they did in that step i marked
like the 1/2
im thinking it was some trig identity but idk
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
Ahhhh i see
alpine sable
Sin2x=2cosxsinx
Thank you
errant dagger
if f ∘ g is injective, is f injective?
lone heartBOT
if f ∘ g is injective, is f injective?
errant dagger
struggling to intuit this or make line diagrams
glacial patrol
either prove or come up with a counterexample
errant dagger
not sure how to prove
and I feel like it should be intuitive
im trying to think like
the outputs of g as inputs may make f of g injective but
other elements within the domain of f may not
glacial patrol
well you were trying to prove that g was injective for example
Then you know there exists a left inverse $h$ such that $h \circ (f \circ g) = id$
ocean sealBOT
992qqoloy
glacial patrol
Which implies $g$ has as left inverse $h \circ f$
ocean sealBOT
992qqoloy
glacial patrol
Which would imply g is injective
Buuut
You're tryna do f
I guess what I'm getting at is that maybe you're struggling for a reason 🤷♂️
Might help if you think of a function f with a different domain than g
errant dagger
@glacial patrol
i tried to produce some sets and wrote out a little proof for my head, does this make sense? consider the function h of g in this case
glacial patrol
looks good
errant dagger
.close
lone heartBOT
errant dagger
!close
lone heartBOT
Available help channel!
silk dome
lone heartBOT
upbeat gorge
Do you know how to evaluate an infinite geometric series?
upbeat gorge
Yes
silk dome
upbeat gorge
No
upbeat gorge
What’s the fourth term in terms of your first term and your common ratio?
think carefully
silk dome
`should of been to the power of 3
upbeat gorge
Ye
silk dome
r =1/3
upbeat gorge
Ye
upbeat gorge
Yep
silk dome
i dont know what it means with the 99%?
upbeat gorge
99% of the sum
silk dome
so you would have to work out 99% of 81 (the sum) then see teh n which goes to that??
silk dome
99% of the sum
if that makes sense?
upbeat gorge
Yep
upbeat gorge
Note that you’re adding stuff also to get to the 80.19
It’s a finite geometric series now
Which has its own formula
silk dome
Which has its own formula
ohh ok
then my final answer would be 4.19 so n would have to round up so 5
upbeat gorge
Yeah that sounds right
tawdry lodge
finding the location of a point based on the distance and slope
minor needle
Can you determine the slope?
tawdry lodge
yeah we have the slope
tacit arch
you can use trig
lone heartBOT
lone heartBOT
Available help channel!
white turret
\cos i
white turret
$\cos i$
ocean sealBOT
A Note
wild umbra
?
vale wigeon
is this just idle curiosity or did you see this in a problem somewhere
golden canyon
$\cos(x) = \frac{e^{ix} + e^{-ix}}{2}$
ocean sealBOT
Jelle
golden canyon
If you draw a picture on a unit circle you see where this comes from
this makes it a bit more clear hopefully:
vale wigeon
is this just idle curiosity or did you see this in a problem somewhere?
golden canyon
If you add e^ix and e^-ix, it is real
digital jay
Hi guys are I have a very simple question about the famous irrational number pi, it's really irrational because the fraction 314/100 = 3.14 or it's juste a question accuracy ?
lunar palm
Hi guys are I have a very simple question about the famous irrational number pi,...
i'm a little unsure as to what you mean
pi is irrational because you can't express it as a fraction, only approximations of it
digital jay
Ah ok
lunar palm
3.14 is an approximation but is not equal to pi
digital jay
It's a question of accuracy
Yes alright 👍
Thank you so much for your quick help appreciate it
lone heartBOT
@digital jay Has your question been resolved?
shy jacinth
Determine the number 𝑡 so that the vectors 𝑎⃗ and 𝑏⃗⃗ are parallel.
slow forum
help
lapis pumice
For the line y = 2x + 4. The y-intercept is [a] and the slope is [b]. What is b?
For the line y = 2x + 4. The y-intercept is [a] and the slope is [b]. What is a?
can anyone help me with this? i cant get the right answer.....
wild umbra
!occupied
lone heartBOT
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
lapis pumice
oh wait sorry wrong channel
gray isle
there are also other issues with your values
gray isle
your point slope form is wrong
$y-y_1 = m(x\ \red{-} \ x_1)$
not +
and again, you need to express it in the desired general form
gray isle
that's something you could use to get an equation of a line using the slope and a point
you'll still need to manipulate the result to general form
slow forum
okay
let me solve for this
i get one more chance xD
can u teach me plz
what i do first get slope rite?
gray isle
yes
gray isle
the choose one of the points and plug that into
$$y-y_1 = m(x- x_1)$$
ocean sealBOT
ℝam()n()v
gray isle
no
you used 5 for y_1 instead of -5
and the way you're laying out the final steps is horrid
drifting beacon
Putting x_1=1, y_1=-5
We have y-(-5) = 8/5 *(x-1)
→ y+5 = 8/5 *(x-1)
The LHS should be y+5
slow forum
still got the same answer
oh wait
its subtraction
after that
-8/5 minutes 5 over 1
drifting beacon
Yes
drifting beacon
Remember that they ask you to give it in general form
General form : Ax + By + C = 0
slow forum
so everything is opposite
so what would a be then
ax
the sign
u make it =0
sign change
gray isle
you should first do multiplication on both sides to rid yourself of fractions
drifting beacon
Now you have y = 8/5 x - 33/5 right?
slow forum
Now you have y = 8/5 x - 33/5 right?
yes
drifting beacon
you should first do multiplication on both sides to rid yourself of fractions
Try doing this
slow forum
gray isle
and ideally you shouldn't write x for multiplication in the presence of variable x
if you insist at least write the variable x cursive
and regardless, you're not multipyling by 5 properly
drifting beacon
$y = 8x/5 - 33/5 \
5y = 8x -33$
ocean sealBOT
Afi
drifting beacon
It should look like this
drifting beacon
$RHS = 5 \frac{8x}{5} - 5 \frac{33}{5}$
ocean sealBOT
Afi
drifting beacon
The 5s would cancel
and give us 8x-33
alpine sable
the most pointless calcualtion known to man kind
can u help me with a vector question
drifting beacon
y not just kjeep it like this
Well that’s because we are asked to give the answer in general form
alpine sable
Well that’s because we are asked to give the answer in general form
can u help me with a vector q from todays 0580 22 paper
drifting beacon
As for 5y = 8x -33
We can simply subtract both sides by 5y
And we have 8x - 5y -33 = 0
Which should be the answer
drifting beacon
can u help me with a vector q from todays 0580 22 paper
Go to the available help channels
slow forum
drifting beacon
Eh you subtract both sides by 5y
LHS = 5y - 5y = 0
RHS = 8x - 5y - 33
So 0 = 8x - 5y -33
slow forum
but i thought u can solve it anyway you'd like
drifting beacon
Well the question asks you to give general form
slow forum
right so just set it to zero and re arrange what does it matter if u add 5 or add 8 and 3?
drifting beacon
Wdym
Ok so the general form is :
Ax + By + C = 0
One side must be 0 so you can’t just randomly add or subtract numbers
slow forum
drifting beacon
It’s -33 not -3
drifting beacon
Rearrange it
8x - 5y - 33 = 0
This is the answer
slow forum
this is the final answer right
?
if i think about the question any longer im gonna have a stroke
slow forum
the last one had y first
part b is asking to graph it
so should i do that using which equation
what
how am i suppose to graph it if the y int is -6.6
the graph only goes to 7 or 6
i guess id round to 7?
gray isle
no don't round anything
use the two given points
and get the line that passes through both of them
gray isle
yes
slow forum
.close
lofty hatch
lone heartBOT
lofty hatch
Can someone explain to me these notations?
pliant cedar
$A=\left(-1+\frac{1}{2},1-\frac{1}{2}\right)\cup\left(-1+\frac{1}{3},1-\frac{1}{3}\right)\cup\left(-1+\frac{1}{4},1-\frac{1}{4}\right)\cup\dots$
ocean sealBOT
SilverSoldier
pliant cedar
C is the same with intersections instead
vague trench
lone heartBOT
vague trench
how would this question be solved
the answer is 100 degrees
i swear the answer is wrong
its 65 degrees
gray isle
what's the question asking for?
b?
vague trench
yessir
gray isle
there is insufficient info to determine that
lethal obsidian
yes
coral flower
lone heartBOT
coral flower
this is what i have so far , but i cant prove it
analog compass
there cant be decimal in decimals
yeah i was abit puzzled
are you doing induction
coral flower
are you doing induction
binomial
<@&286206848099549185> been about 15 mins , no help arrived D:
coral flower
and what is 3.5.7???
3x5 = 15
15x7 = 95
and i wrote 105 
wait no its 105, im right
coral flower
Induction?
how would i use induction ?
drifting seal
prove f(1) is true, then prove f(k+1) is true
analog compass
but the thing is, y is alr defined
coral flower
what is f(x)?
coral flower
@drifting seal pls ping when u have something that can help me , im stuck at this D:
drifting seal
sure...
coral flower
if nothing then no worries , ty for trying 
drifting seal
@coral flower ik how to do
First
solve the quadratic equation
it should have two answer, forget the answer that is negative, y = 1.828427...
Now, prove the statement is equal to this
coral flower
that doesnt affect me , the work i did is correct
so the answer would eventually end up to what i have
drifting seal
I'm guessing to do this with contradiction...
coral flower
im still confused tho
if i find the values of y
i still do the same procedure , same way
so it doesnt matter
drifting seal
Write the general term for y
drifting seal
y = -1 +- sqrt(11)
coral flower
oh that , the values of y from quadratic formula
drifting seal
Yes
and ofc it should be plus for that
-1 + sqrt(11)
Then use contradtiction? idk
coral flower
but the question asks me to find y from the series and then use it in the quadratic as the proof
drifting seal
ys ik
u find the answer from the quad eq
then compare to the series
still good
coral flower
-1 + sqrt(11) = 3/4 + 3.5/4.8 + 3.5.7/4.8.12 + ....... ??
coral flower
sqrt11 = 1 + 3/4 + 3.5/4.8 + 3.5.7/4.8.12 + .......
i can prove that (maybe)
@drifting seal wait dont u just get this answer again?
thats the binomial all summed up
sqrt 11 is not equal to cube root 4
that means this question is freaking wrong
oh finally im free , this question eaten all my brain
drifting seal
HUH
WAIT
Let me check that
ok u can close this first I will help checking that later like tmr
coral flower
how long is it tmr at ur place?
cuz i wanna know if im wrong or question wrong kinda quick :)
lone heartBOT
@coral flower Has your question been resolved?
drifting seal
how long is it tmr at ur place?
8hr later
lone harness
change of variables first
so 2/x+2/y+2/z >= (9*2)/(x+y+z))
no 2(a+b+c)=x+y+z
yeah that could work
all positive real numbers?
also I think the sub x=(a+b)/2 y=(b+c)/2 z=(a+c)/2 is slightly neater
I did it slightly differently
lone harness
also I think the sub x=(a+b)/2 y=(b+c)/2 z=(a+c)/2 is slightly neater
I did this sub
then you get 1/y+1/z+1/x >=9/x+y+z
then multiply through by x+y+z
then you get 1+1+1+(x/y+y/x)+(x/z+z/x)+(y/z+z/y) >=9
can you see how to finish from here?
if you can prove that x/y+y/x >=2 and x/z+z/x>=2 and y/z+z/y >=2 you are done right?
since then 2+2+2+3=9
then
you really just want to prove that u+1/u >=2 for any positive real number u
which is quite easy right?
since you get u^2-2u+1>=0
(u-1)^2>=0
nice
yeah
lol
what are the | you do
im not sure how the second line follows from the first
how does the rhs become 9?
x+y+z != xyz
it's fine it happens to me asw sometimes
yeah these questions are usually quite messy too
lone harness
so 2/x+2/y+2/z >= (9*2)/(x+y+z))
btw this sub works it simplifies to the same thing I've just realised I made a typo here
it should be 9*2 on the numerator instead
as in if you wanted to use my original sub
lone harness
this was my method with the other sub
you don't need to multiply by xyz here
makes the algebra quite long
change of variables are nice when your inequalities are symmetric
then try and clear denominators where it makes sense
if you had something involving 1/xy+1/yz+1/xz then multiplying by xyz makes more sense
yep
I think it's worth learning about AM-GM
have you heard of it?
I think if you search up elementary inequalities olympiads or something similar you'll find quite a few
here's a page
ex. 1.24 is what we used to finish your problem
safe tartan
What would be the x^n term in (1+x)^2n
lone heartBOT
What would be the x^n term in (1+x)^2n
safe tartan
In terms of nCr or ( )
wind cloak
So you need T_(n + 1)
ocean sealBOT
jan Nejon
wind cloak
so it should be 2nCn?
yeah
wind cloak
since a^r needs to be a^n so if r=n yeah idk
yes
wind cloak
$2\sum_{k = 0}^n ^nC_k$
ocean sealBOT
jan Nejon
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
safe tartan
(1+x)^n(1+x)^n, would the coefficient of x^n be (nC0 x nCn) + (nC1 x nCn-1) until (nC0 x nCn) again
wind cloak
yeah
safe tartan
so it shoul dbe
that sum above right
ah shoot
its multiply not plsu
ty so much
.close
silk crag
Easy one but I need an explanation please
lone heartBOT
Easy one but I need an explanation please
fervent timber
try to see if you can get (something)^2 under the square root sign
steady mantle
hint: 47 = 4*11 + 3
silk crag
Where does the +3 go though
silk crag
try to see if you can get (something)^2 under the square root sign
That's the thing, idk what to ² under the √
alpine nacelle
when you don't know how to work from the top, work from the bottom
2sqrt(11)-sqrt(3) = sqrt(44)-sqrt(3)
= sqrt((sqrt(44)-sqrt(3))²) = ...
silk crag
when you don't know how to work from the top, work from the bottom
2sqrt(11)-sqr...
I can't because I need to do it by not looking at the answer
alpine nacelle
yeah but if you understand one direction, you'll understand the other
just take the equalities in reverse and you'll see what was the idea
and you'll link it to Toblerone's hint
wise kayak
Unsure how to write statements using logic quantifiers and connectives (mainly which connective to use and where) if anyone could help me understand how to read a statement then convert it to logic symbol form it would be appreciated
wise kayak
Example, we got given this problem to do in todays lecture to help us understand proper use of logic symbols but I’m unsure what to write (this is not a graded piece of work do)
Dw*
I got this as the answer but I’m unsure if I’ve used the proper connectives (in this case &)
lone heartBOT
@wise kayak Has your question been resolved?
wise kayak
<@&286206848099549185>
magic scarab
why do i keep being pinged
unkempt vapor
I got this as the answer but I’m unsure if I’ve used the proper connectives (in ...
yeah, but not sure about first 2 brackets
wise kayak
What is wrong with them?
unkempt vapor
I didn't think you had to do an & there
is there any resource you use?
wise kayak
Just going off lecture notes and exercises we did in class
unkempt vapor
ok
wise kayak
Could I write it like this for 1st two brackets?
unkempt vapor
i guess this is right though
unkempt vapor
Could I write it like this for 1st two brackets?
don't think so
wise kayak
When would I use a => sign when trying to write statements like these?
wise kayak
don't think so
Oh really, why’s that?
unkempt vapor
Oh really, why’s that?
looks weird, intuition
unkempt vapor
When would I use a => sign when trying to write statements like these?
it's something like, If A, then B; A => B
if a>0 => a+1>1
wise kayak
The negation of A => B would be notB => notA ?
Couldn’t find the proper symbol on my keyboard hahaha
unkempt vapor
The negation of A => B would be notB => notA ?
hmm
wise kayak
if a>0 => a+1>1
So the negation of this is a+1<1 => a<0 I think?
unkempt vapor
So the negation of this is a+1<1 => a<0 I think?
right
group theory
if A is part of B, then !B is part of !A
unkempt vapor
So the negation of this is a+1<1 => a<0 I think?
btw, this is <=> (in this case)
unkempt vapor
If and only if?
yeah, that's what i was thinking of
wise kayak
if A is part of B, then !B is part of !A
But for other cases this is the negation of => ?
unkempt vapor
But for other cases this is the negation of => ?
mostly
example
|x|>0 and x>0
what is the relation?
wise kayak
x > 0 => |x| > 0 ?
unkempt vapor
x > 0 => |x| > 0 ?
right
wise kayak
Not all the time |x| implies a positive x value?
unkempt vapor
unless 0
unkempt vapor
|-2|=4?
unkempt vapor
you mean |-2|=2?
unkempt vapor
Modulus of -2 isn’t 4?
nah
unkempt vapor
right
wise kayak
Got it, thanks for helping me
lone heartBOT
@wise kayak Has your question been resolved?
zenith belfry
Some help with this would be appreciated. I know G is cyclic if it is generated by an element, but I'm not sure how to determine if it is cyclic from the order. Reply to this message or @ me with any responses if you wouldn't mind!
lone heartBOT
Some help with this would be appreciated. I know G is cyclic if it is generated ...
@zenith belfry Has your question been resolved?
lone heartBOT
@zenith belfry Has your question been resolved?
zenith belfry
<@&286206848099549185>
twin nimbus
@zenith belfry hint, can you prove that disjoint cycles commute?
lone heartBOT
@zenith belfry Has your question been resolved?
zenith belfry
<@239527279489712128> hint, can you prove that disjoint cycles commute?
Fairly easily, yeah
twin nimbus
So if (st)^n = s^n t^n, and |s| = a, |t| = b, then it would make perfect sense for the cycle length to be lcm(a, b) yeah?
We want the smallest number k such that t^k = e and s^k = e
(This will be a multiple of a and b, and the smallest such multiple, so the lcm)
@zenith belfry
zenith belfry
So if (st)^n = s^n t^n, and |s| = a, |t| = b, then it would make perfect sense f...
That makes sense.
Then we'd have to show there's no m<k?
twin nimbus
Yeah, but that's pretty easy, because s and t are disjoint, (st)^n = e if and only if s^n = e and t^n = e
twin nimbus
Yw
zenith belfry
.close
lone heartBOT
Available help channel!
ruby topaz
lone heartBOT
ruby topaz
my friend asked me it
oh i asked it earlier today
but i never got much answer
so i am asking again
that might be why
golden canyon
ruby topaz
oh weird
idk where its from
my friend just keeps asking me if i can find out
i know they asked it after i asked it on a chat
but ill have a look at that
golden canyon
Im not sure about the problem, but https://discord.com/channels/268882317391429632/903486480985489478 seems to have found something
lone heartBOT
@ruby topaz Has your question been resolved?
lone heartBOT
@ruby topaz Has your question been resolved?
ruby topaz
<@&286206848099549185>
ruby topaz
yeh but what do i do with it
lone heartBOT
@ruby topaz Has your question been resolved?
velvet elm
i need help finding the particular of this relation
lone heartBOT
i need help finding the particular of this relation
trim tendon
$\exists xP(x)\equiv \neg\neg(\exists xP(x))\equiv\neg(\forall x\neg P(x)) \equiv \neg(\forall x) p(x)$
trim tendon
ocean sealBOT
Kalgar
trim tendon
What's wrong with my working in predicate calculus?
where did I go wrong with the rules/
placid zinc
Where did the ~ inside go? It disappears on the last line
trim tendon
Where did the ~ inside go? It disappears on the last line
I distributed the ~ into the brackets
to both the forall and the P(x)
so I got ~~p(x)
= p(x)
placid zinc
I'm not following the justification. Anyway, this is the incorrect step.
trim tendon
I'm not following the justification. Anyway, this is the incorrect step.
what
can't you distribute ~ into brackets
~(p(x)) = ~p(x)
and ~\forall = exists
placid zinc
I don't see any distribution, I see a ~ disappearing
ocean sealBOT
Kalgar
trim tendon
then negate the $\neg P(x)$
ocean sealBOT
Kalgar
trim tendon
but $\neg \neg P(x)$ is just regular $P(x)$
ocean sealBOT
Kalgar
trim tendon
negations cancel
placid zinc
"forall x" isn't a statement, and can't be negated
You can pass a negation over it, but you get a "there exists" if you do
"for all x, ~P(x)" is the statement, it has a negation on it
trim tendon
You can pass a negation over it, but you get a "there exists" if you do
so why is this step correct?
trim tendon
.
but I did the same thing here
same reasoning
!
where is what negation dissappearing?
placid zinc
You're negating something that isn't a statement
ocean sealBOT
Kalgar
placid zinc
In step 3
The leftmost ~ applies to the whole thing already
trim tendon
isn't that how you negate quantifiers with logic rules
wait
is this notation negating the entire statement
this first negation
i.e. $\neg (\forall x \neg p(x))$
ocean sealBOT
Kalgar
placid zinc
trim tendon
I'm so confused
placid zinc
Your rule for step 3 to step 4 seems made up
placid zinc
You're trying to put an operation between "for all x" and ~P(x), and then trying to say that ~ can distribute over that
trim tendon
does the brackets here have any significance?
why are they putting brackets over the quantifiers
trim tendon
are you explaining this really badly or am I like just dumb ;-;
placid zinc
There's a few differences between what you did and the DeMorgan's law:
- Your "for all" didn't turn into a "there exists"
- The ~ didn't pass through the quantifier, but stayed to the left of it
trim tendon
"Your "for all" didn't turn into a "there exists""
yeah but I put a negation in front of it
placid zinc
Where it was before lol
trim tendon
placid zinc
Both are to the left of the "for all", so it hasn't moved
The bracketing doesn't matter, which might be throwing you off
trim tendon
Both are to the left of the "for all", so it hasn't moved
I mean like
placid zinc
I suggest trying to find where you got this rule
trim tendon
$2(a+b)=2a+2b$
that
that's basically what I did
distribute the negation symbol into the brackets to remove the outer brackets
ocean sealBOT
Kalgar
placid zinc
Okay, so that's saying that multiplication distributes over addition. I agree with that
Your example is saying negation distributes over... what, exactly?
trim tendon
Your example is saying negation distributes over... what, exactly?
every quantifer and proposition in some statement
these two parts
both negated individually
so $\exists x P(x)$
ocean sealBOT
Kalgar
trim tendon
isn't that what this bracket notation they're using means?
otherwise wtf is it representing here
why not make it clear ~(...) negating the entire thing if that's what they mean
placid zinc
No. They mean
"We're taking the negation of the statement 'for all x, not p(x)'"
Indeed, the bracketing means nothing
trim tendon
No. They mean
"We're taking the negation of the statement 'for all x, not p(x)'"
are these two the same thing then?
first negation negates entire statement
placid zinc
Yes I read those to be the same