#They say numbers can be positive and negative, right?

205 messages · Page 1 of 1 (latest)

ivory tinsel
#

But except for 0 since it cannot be positive and negative, but what happens if:

289_20240209000210.png 289_20240209000124.png
pliant sparrowBOT
empty umbra
#

Positive is defined as "greater than 0" and negative is defined as "less than 0". But 0 is neither greater than nor less than itself.

ivory tinsel
empty umbra
#

0+0=0-0=0

ivory tinsel
empty umbra
#

You can write +0 or -0, but +0=-0=0

ivory tinsel
empty umbra
#

Are either of them equal to 0?

ivory tinsel
empty umbra
#

and -0 is something different?

ivory tinsel
#

But

#

0 ≠ -0

#

And

#

+0 ≠ -0

#

What would happen?

#

Nothing?

empty umbra
#

Depends.

#

The real numbers come with a large number of properties

#

But a good number of those properties depend on there being a unique 0 element

#

So you would have to give up one of those many properties

#

associativity
total order
completeness
commutativity

#

Which one(s) you lose depends on how you would define -0

ivory tinsel
empty umbra
#

completness property would say that there must be

ivory tinsel
empty umbra
#

completeness property just says that "between any two unequal numbers, exists another number"

#

Or maybe that denseness property? I forget

ivory tinsel
empty umbra
#

Yeah, it's denseness

ivory tinsel
#

Oh okay

#

And there is another question

#

This is of course off topic, but I would like to know

empty umbra
#

So, for real numbers to remain dense, a number must exist between -0 and +0. And whatever number that is, a number must exist between that and -0, and between it and +0, and so on indefinitely

ivory tinsel
#

Interesting

#

Okay

empty umbra
ivory tinsel
#

I came up with a number

ivory tinsel
ivory tinsel
empty umbra
#

What does it do?

ivory tinsel
#

This number can be anything

empty umbra
#

And what can you do with that?

ivory tinsel
#

It may be equal to...
C = 1
C = 4
C = -1
C = 0.5
C = Pi
C = sqrt(-1)
C = infinity
Etc...

empty umbra
#

Okay, but what can do you with it? What utility does it serve?

ivory tinsel
empty umbra
#

btw infinity is not a number. And sqrt(-1) is not a (real) number

#

I would say there's very little you could do with it.

ivory tinsel
empty umbra
#

If anything, you've just described a variable

#

But yours is a bit worse than a variable, because it breaks even reflexive property of equality.
$$C\ne C$$

ivory tinsel
vocal frigateBOT
empty umbra
#

That's pretty harsh

ivory tinsel
ivory tinsel
empty umbra
#

I would say very little, if anything

ivory tinsel
#

Break the math?

#

😅

empty umbra
#

You lose almost everything the real line offers

#

You break the math of your own structure

#

you built a castle out of dry sand and are seeing it crumble before you.

ivory tinsel
#

🤔

ivory tinsel
empty umbra
#

I would say nothing

ivory tinsel
empty umbra
#

But it's your idea. But the onus of its utility falls on you, my friend.

ivory tinsel
empty umbra
#

If you want to draw the whole plane, you could just write $\bR^2$

vocal frigateBOT
ivory tinsel
#

Or C

#

?

empty umbra
#

C and R² are different (though pretty similar) structures

ivory tinsel
empty umbra
#

Do you mean C as in your thing, or as in complex numbers?

ivory tinsel
#

That's literally all

empty umbra
#

Oh then they're very different

#

Not at all the same

#

If C is everything, then you can literally do nothing with it, because you've introduced no refinement, no structure, no boundary

#

Basically, you're in nothingness because there is no separation between truth and fiction now

ivory tinsel
empty umbra
#

end of story

#

There's nothing you can do with it

#

It's like saying "everything is true no matter what"

#

Then no useful deductions can be made, because it always evaluates to truth

#

We can't do anything with that

ivory tinsel
#

C > infinity?

#

Apparently I broke you?

#

In general it cannot > < or =

empty umbra
empty umbra
# ivory tinsel C > infinity?

This is more nonsense as

  1. infinity is not a number
  2. if it were, it has no ordering attached to it (at least in these simple terms)
#

I won't stop you from playing with your little toy, but I'm simply letting you know that, as far as it's been described now, it's pure nonsense.

ivory tinsel
empty umbra
#

Technically, nothing is "wrong" when you try to defined a structure in math. The real question is how useful it is. And so far, I've seen no use from what you've shared

ivory tinsel
#

I did a lot of interesting things, but at the same time it's useless...

ivory tinsel
empty umbra
#

I will say, at the very least, it sounds like what you were trying to describe was just a free variable, but there were a lot of problems with your definition.

ivory tinsel
#

I just did it fantastic

empty umbra
ivory tinsel
ivory tinsel
#

Or can this be proven? Hmm 🤔

#

But I'm too small but I can still try

empty umbra
#

Given a circle, you cannot construct (using only a compass and straightedge) a square of equal area

ivory tinsel
#

Maybe

empty umbra
#

That's the only thing that sounds close to what you said

ivory tinsel
empty umbra
#

exactly what I said

ivory tinsel
empty umbra
#

which part?

ivory tinsel
#

All

empty umbra
#

Do you know what construction with a compass and straightedge is?

ivory tinsel
#

Yeah

empty umbra
#

So do you know how to construct a square?

ivory tinsel
empty umbra
#

aka ruler

ivory tinsel
empty umbra
#

also known as a ruler

red oxide
empty umbra
#

we're not friends

#

I'm simply a helper

#

I don't keep friends in this server save for one or two folks I've known for a while

ivory tinsel
#

My English is terrible

#

I don't understand

empty umbra
ivory tinsel
#

And?

empty umbra
#

and what?

#

Why what?

empty umbra
ivory tinsel
ivory tinsel
#

No?

empty umbra
#

Okay. I have no interest in helping if we're just going to devolve into nonsense. Good luck to you.

ivory tinsel
#

Oh okay

red oxide
#

are you over excited about math, MediaS?

ivory tinsel
#

Yes

red oxide
#

That's what I see everytime you open a thread

ivory tinsel
#

Lately I've become very interested

red oxide
#

You see something new and it makes BOOM in your body

ivory tinsel
red oxide
#

If you wanna learn math for real, buy some books and do some self study

ivory tinsel
red oxide
#

If you jump from topic to topic without really learning the basics you won't get far

#

Learn 1 topic, stick to it, and then if you are confident, or gained some knowledge, go tothe next

ivory tinsel
red oxide
# ivory tinsel What books do you recommend for me?

https://youtu.be/fb_v5Bc8PSk?si=TVOINZefLdF2PG7R

YouTube
The Math Sorcerer
How To Self-Study Math

In this video I give a step by step guide on how to self-study mathematics. I talk about the things you need and how to use them so that you can make the best use of your time.

The pencils: https://amzn.to/3PazT6e
The pen: https://amzn.to/3Pbq7R6
The paper: https://amzn.to/3d6FoVZ
The timer: https://amzn.to/3p3ePE2
The calculus book: https://am...

▶ Play video
ivory tinsel
#

I don't know, I just want to learn something new and interesting

red oxide
ivory tinsel
red oxide
#

and take some notes

ivory tinsel
#

How did you become such a smart mathematician? Where did you start?

red oxide
#

There 1000x more people on this server more competent and smarter than me

#

but i guess the key is persistence and patience with yourself

ivory tinsel
red oxide
#

to get a grasp of thing in your own

red oxide
ivory tinsel
#

Even I can’t learn this at 16, although I would like to

red oxide
#

You should first start with Calculus then

#

which will lead you to that topic

ivory tinsel
ivory tinsel
#

But it's a very simple sign

#

Also with П

red oxide
#

prob not

#

maybe mentioned

#

But those are just notations

#

to make big things short and compact

ivory tinsel
red oxide
ivory tinsel
#

Um

#

Yes?

red oxide
#

you mean Greek symbol?

ivory tinsel
#
    • × ÷ sigma etc
#

Z

red oxide
#

ok so you mean any arbitrary symbol

ivory tinsel
vocal frigateBOT
#

adonhs

587715738484211754.png
ivory tinsel
#

Good

#

Although I still don't understand how it works 😅

red oxide
ivory tinsel
#

Okay

red oxide
#

i am going off, good luck on learning!