There are an infinite number of real numbers between any two real numbers

>infinite precision maths in a universe where numbers cannot have infinite precision

Pretty simple desu

Once you get to extremely small numbers, mathematical laws and behavior will start to break down. That's kind of what Calculus is starting to get at, when you have "soft zeroes" that aren't really zero.

then how many real numbers are there between any two (distinct) real numbers??

It's all conceptual, don't think too hard about it

Stupid phoneposter.

We don't know where it breaks down. Probably somewhere far below the Planck Scale in a realm we may not be able to physically study. Really we would need a new field of Quantum Number Theory, and to my knowledge no one is studying that.

wow i don't know how i will recover from such a devastating accusation

It's actually more of a statement. You are a phoneposter, that's just how it is.

As for the stupidity, it doesn't really matter what you think.

Probably about 68.

It's unbelievable to read something like this. Did someone like you did studies in science or are you just reading pop-sci?

>he fell for cantor's diagonal argument

damn am i being roasted...?

All of that stuff is completely irrelevant to the enterprise of mathematics, though.

Yes.
You are being told.

Even if this were true, it wouldn't make the current theory of real numbers wrong, just inadequate for studying the phyical universe in full precision. "Right" and "wrong" in mathematics has absolutely nothing to do with the real world.

It's not. What is the point of a number if you can't even do anything with it in this universe? It might logically exist with the overall framework, but in no other sense is it a thing.

>wildberger.png

So, we have Planck distances, where at smaller distances all of our physics breaks down and we can't reliably describe what happens.

Couldn't we have, say, a Planck number, where we can imagine smaller numbers but none of our math really applies anymore in any meaningful way?

>implying there's a point to maths

there isn't
math doesn't have to model anything
it just does sometimes

kinda exists
look up infinitesimal calculus

pi = 4 sum from k=1 to inf of (-1)^(k+1)/(2k-1)

Get rekt wildburger.

>[THIS IS WHAT UNDERGRAD ENGINEERING MAJORS ACTUALLY BELIEVE]

Reminder that there is nothing to suggest that space is quantised.

The "Planck Length is the smallest distance" meme was started by some Russian crank who edited his bullshit theory into the wikipedia article.

>this is what unemployable math PhD students believe

P doesn't equal NP, spergs

Kek'd

>all these engineering students who think applied math and real math is the same thing

>maths students

[math]\mathscr{P}(\mathbb{C})[/math]
Where's your God now?

That's weird. Displayed fine before posting. Lemme try this again.
[math]\mathscr{P}( \mathbb{C} )[/math]

this post triggers me. we dont know if space is discrete or not

[math]\mathscr{P}^n( \mathbb{C} )[/math]

OP obviously meant "two different real numbers"
but you wanna play, apparently.

Let's play, then.

0.5 doesn't mean a thing.
You have to define what "." mean.
I assume it marks the units, as you are a classical retarded faggot in here.
Then, what is your system of counting?

So: an infinity number of numbers could fit between the two writings you produced of what I guess being numbers.

Feck off now with your certainties.

Checkmate undone, outrageously boring stupid player kicked out of the game.

More like
>infinite number of real numbers between any two real numbers
It's infinity what your trying to grasp can't be grasped without dmt
Also if you do dmt and any scary entities appear (trip hack) ask them about themselves to make them disappear

yeah right
go teach dmt to cantor

poor postmodern fag

thinking he has any kind of knowledge
where he doesn't have any

I'm no expert on infinite sets you caught me. I failed to specify that you can have existential knowledge and understanding of infinity with dmt (or high dosage lsd)

>existential knowledge
Knowledge which is not knowledge.

>Someone who will never have a strong enough philosophical mindset to solve a substantial problem or make substantial progress

Did Sarah the super scientist gain knowledge... or merely experience?

Are you trying to twist me into segueing that you shouldn't pursue more of both simultaneously to maintain a proper context for thinking and problem solving? Because I won't do that

Arguing whoops

Why would it be a problem that some mathematical concepts don't correspond to anything physical? Assuming you aren't just baiting with Wildburger and his numbers that don't fit the universe.

lol mad

It's not true. E.g. there are no real numbers between 12 and 12.
However it's true for any two distinct real numbers.

>empty set
>not infinite

OK

>mfw when i didn't put a new constant C after adding two distinct integrals

hehe im a little devil bastard am i?

This is actually really good bait.

user you went too far!

Yes, there's no experimental evidence. There are some unproven theories of quantum gravity that assume it, though.

I tend to think it isn't.

There is more real numbers between 0 and 1 than there are integers

prove it.

So infinity > infinity? dunno bout that my man

[math] 2^{\aleph_0} > \aleph_0 [/math].

We show that there is no bijection between a set [math]S[/math] and its powerset [math] 2^S [/math].

Suppose there such a function [math] f: S \rightarrow 2^S [/math].

Let [math] X \subset S [/math] be [math] \{ x \ | \ x \notin f(x) \} [/math].

Because [math] f [/math] is a bijection, there is some [math] x [/math] such that [math] f(x) = X [/math]. Is [math] x \in X [/math] ? If it is, then by definition of [math]f[/math] it isn't. And if it isn't, then it is. Contradiction.

As clearly the [math] [0,1] \subset \mathbb{R} [/math] is in bijection with the powerset of [math] \mathbb{N} [/math] by associating to each subset its indicator function as a binary representation (modulo countably many equivalences), there are thus more real numbers between [math]0[/math] and [math]1[/math] than there are integers.

>yfw you realize there really are fewer even integers than integers, since the even integers are a proper subset of the integers

>Rei

Concentrate on the facial expression, garbageman

Not true, you can draw a 1-to-1 correspondence between even integers and all integers. They are the same "size".

>falling for bait

>I was only pretending to be a moron!

His image made it obvious. It was a joke.

What? No it doesn't.

So what? I can draw functions all I want. One is a proper subset of the other; case closed

Consider the power set of the reals P(R)
If you were to take the infinitely recursive power set of it, i.e. P(P(P(P(...P(R)...))))

The order of that resulting set is SO LARGE, not only is it uncountable, but it literally isnt even a number
We have absolutely no way of understanding how large it is

So in other words, the real number line is THICC? Is that what you're trying to say?

Irrelevant as to whether they are the same size. Just line them up, n on one side, 2n on the other, and you'll see that there is a 1-to-1 relationship, in other words, they are the same size.

1 : 2
2 : 4
3 : 6
4 : 8
n : 2n

It's called [math]\beth_\omega[/math].

What the fuck did you just fucking say about complex numbers, you little bitch? I’ll have you know I stopped caring about math when I was introduced to the concept of imaginary numbers, and I’ve been involved in numerous secret raids on Al-Gebra, and I have over 300 crocks of shit. I am trained in equations that can only be solved by inventing numbers that can't exist and I’m the top math deity in the entire US academic forces. You are nothing to me but fucking wrong. I will wipe you the fuck out with math the flaws of which have never been seen before on this Earth, mark my fucking words. You think you can get away with saying that shit to me over the Internet? Think again, fucker. As we speak I am contacting my secret network of algebra solutions across the USA and your IP is being traced right now so you better say "the correct answer is whatever the correct answer is", maggot. The math that says the pathetic little thing transcribed to words. You’re fucking dead, kid. I can be anywhere, anytime, and I can mark you wrong in over seven hundred ways, and that’s just if you write it down in english instead of ancient math runes. Not only am I extensively trained in unarmed combat, but I have access to the entire arsenal of the United States Logical Math Corps and I will use numbers that never lie to their full extent to wipe your miserable ass off the face of the continent, you little shit. If only you could have known what unholy flaws your little “clever” human construct was about to bring down upon you, maybe you would have held your fucking tongue. But you couldn’t, you didn’t, and now you’re paying the price, you goddamn idiot. I will shit complex numbers all over you and you will drown in it. You’re fucking dead, kiddo.

>>
>then how many real numbers are there between any two (distinct) real numbers??
huh, you have not checked the work. the answer is 1000^10^200

Kek are you actually autsitic?

Who fucking cares, we can't see smaller things past a certain poin and very large thing shroud what's behind it like the universe.

This is just sad to read, you are an autist and a retard, OP didn't mention that the two numbers are distinct.

>there are the same amount of reals between two arbitrarily closed real numbers than in the whole number line

>Thinks we are limited by THIS universe when the true nature of existence is infinite.
This is true;
spiritually,
physically and,
mathematically.
Fucking pleb

lmaooo u mad white boi?

I wandered into this thread because I was anticipating large rumps, but I honestly must tell you that I have absolutely no fucking idea what you're arguing about.

Why are there numbers in between numbers and what makes that infinite?

Let's take x to be a plank number. Then x/2 is smaller than plank number and is meaningful

I only accept infinities that can be modeled with infinite hotel rooms

define "define"

Nope. Sorry little boy, the world isn't a magic place of infinite possibility. It's a cold, hard, vicious, finite space.

Distances smaller than planck distances don't need to exist for us to represent them by extrapolating our number system. Negative apples don't exist, but we can do negative math on apples. There is not an infinity of particles but we have a mathematical concept of infinity which has applications.

Mathematics is not concerned with the physical world and therefore mathematicians are not concerned. I think the people whom you are complaining about are physicists.

The real numbers have nothing to do with physics. It is quite simple to prove you can always find a real number between any two real numbers.

>planck scale
>counting
>quantum number theory

Oh my God I can hear how stupid you are

kek

when you realise that infinitely small is still a value

you'll understand what they meant by space is quantized

>russel
your meme
is
nothing
funny

It's spelled Russell with two L' you brainlet

>dark numbers

Wow. Memeberger stepped up his game since I last checked his videos!

> with two L' you brainlet
I must admit I keked, because one writes "two L's".
You must be the king of the retards slugging their way in this shit board.
Furthermore, I must have taught you something about logic, which I'm glad for. Generally, when attacks spot orthographical issues - especially for surnames - it means the poster is feeling weak on others level.

No experimentally backed up theory suggests that space is quantised