>there are an infinite number of real numbers between

>>8371880
>imokwiththis.jpg

File: image.jpg (30KB, 240x255px) Image search: [Google]

30KB, 240x255px

>there an infinite number of integers
>there are more real numbers than integers

>>8371880
Probably not. Eventually we'll have to accept that the universe doesn't afford infinite precision, and has no truly continuous features. It is all quantized.

It's physically impossible to represent a number of infinite precision. It cannot be done.

>>8371880
>[math] | \mathbb { N } | = | \mathbb { Q } | [/math]

>>8371890

mathematics isn't based in the physical world retard

>>8371893
Have fun trying to do math the universe isn't capable of doing.

>>8371880
How many numbers are there between 0.5 and 1/2? Checkmate mathtard

File: image.jpg (37KB, 349x642px) Image search: [Google]

37KB, 349x642px

>>8371900

>math the universe isn't capable of doing

what does the even mean

>>8371912
Think a little bit about information and machinery, then get back to me. The universe, unfortunately, isn't the magic feel-good land of infinite possibility mathematicians seem to want it to be. There are hard limits to what the universe allows.

Silly /sci/. Not realizing the universe is a finite state machine.

>>8371912
>infinite precision maths in a universe where numbers cannot have infinite precision

Pretty simple desu

>>8371912
>>8371893

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.

>>8371922
>>8371919
>>8371918

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

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

>>8371912
Stupid phoneposter.

>>8371924
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.

>>8371935

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

>>8371942
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.

>>8371924

Probably about 68.

>>8371936
It's unbelievable to read something like this. Did someone like you did studies in science or are you just reading pop-sci?

File: 1470830428369.jpg (56KB, 585x599px) Image search: [Google]

56KB, 585x599px

>>8371885
>he fell for cantor's diagonal argument

>>8371948

damn am i being roasted...?

>>8371918
All of that stuff is completely irrelevant to the enterprise of mathematics, though.

>>8371990
Yes.
You are being told.

>>8371936
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.

>>8371993
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?

>>8372001
>implying there's a point to maths

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

>>8372035
kinda exists
look up infinitesimal calculus

>>8371890
pi = 4 sum from k=1 to inf of (-1)^(k+1)/(2k-1)

Get rekt wildburger.

>>8371918
>[THIS IS WHAT UNDERGRAD ENGINEERING MAJORS ACTUALLY BELIEVE]

>>8371890
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.

>>8372058
>this is what unemployable math PhD students believe

>>8371880
P doesn't equal NP, spergs>>8371880

>>8371901
Kek'd

File: 1468027310891.jpg (19KB, 480x547px) Image search: [Google]

19KB, 480x547px

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

File: image.png (29KB, 712x526px) Image search: [Google]

29KB, 712x526px

>>8372291
>maths students

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

>>8372311
That's weird. Displayed fine before posting. Lemme try this again.
[math]\mathscr{P}( \mathbb{C} )[/math]

>>8371890
this post triggers me. we dont know if space is discrete or not

>>8372317
[math]\mathscr{P}^n( \mathbb{C} )[/math]

>>8371901
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

>>8372419
yeah right
go teach dmt to cantor

poor postmodern fag

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

>>8372452
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)

>>8372485
>existential knowledge
Knowledge which is not knowledge.

>>8372490
>Someone who will never have a strong enough philosophical mindset to solve a substantial problem or make substantial progress

>>8372504
Did Sarah the super scientist gain knowledge... or merely experience?

>>8372510
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

File: 3456945563_a9b52c43b4.jpg (100KB, 404x500px)

100KB, 404x500px

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.

>>8372388
lol mad

File: IMG_2558.jpg (175KB, 1024x1276px) Image search: [Google]

175KB, 1024x1276px

>>8371880
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.

>>8372577
>empty set
>not infinite

OK

>>8372577

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

hehe im a little devil bastard am i?

>>8371890
This is actually really good bait.

File: IMG_2559.jpg (50KB, 357x376px)

50KB, 357x376px

>>8372605
Anon you went too far!

>>8372059
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

>>8372972
prove it.

>>8372972
So infinity > infinity? dunno bout that my man

>>8373098
[math] 2^{\aleph_0} > \aleph_0 [/math].

>>8372996
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.

File: brown-cotton-suit-blue-bengal-stripe-shirt-no-tie-mens-summer-business-casual-outfit-idea-7.jpg (114KB, 664x996px) Image search: [Google]

114KB, 664x996px

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

>>8372563
>Rei
>>>/trash/

File: 87966.jpg (107KB, 780x780px) Image search: [Google]

107KB, 780x780px

>>8373161
Concentrate on the facial expression, garbageman

>>8373138

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

>>8373196
>falling for bait

>>8373205
>I was only pretending to be a moron!

>>8373211
His image made it obvious. It was a joke.

>>8373214

What? No it doesn't.

>>8373196
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

>>8371880
So in other words, the real number line is THICC? Is that what you're trying to say?

>>8373257

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

>>8373299
It's called [math]\beth_\omega[/math].

>>8371880
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.

File: 1446500811839.jpg (211KB, 1920x1080px) Image search: [Google]

211KB, 1920x1080px

>>8371924
>>
>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

>>8372388
Kek are you actually autsitic?

>>8371880
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.

>>8372388
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

>>8371918
>Thinks we are limited by THIS universe when the true nature of existence is infinite.
This is true;
spiritually,
physically and,
mathematically.
Fucking pleb

>>8372388
lmaooo u mad white boi?

>>8371880
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?

>>8372035
Let's take x to be a plank number. Then x/2 is smaller than plank number and is meaningful

>>8371978
I only accept infinities that can be modeled with infinite hotel rooms

>>8372388
define "define"

>>8376080
Nope. Sorry little boy, the world isn't a magic place of infinite possibility. It's a cold, hard, vicious, finite space.

>>8372035
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.

>>8371919
>>8371922
>>8371918
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.

>>8371936
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.

>>8371936
>planck scale
>counting
>quantum number theory

Oh my God I can hear how stupid you are

>>8372059
kek

when you realise that infinitely small is still a value

you'll understand what they meant by space is quantized

>>8376266
>russel
your meme
is
nothing
funny

>>8377951
It's spelled Russell with two L' you brainlet

>>8373755
>dark numbers

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

>>8378180
> 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.

>>8376403
No experimentally backed up theory suggests that space is quantised

File: Mike-Tyson-clapping-and-laughing[1].gif (4MB, 320x180px) Image search: [Google]

4MB, 320x180px

>>8371890
>mathematics
>physically impossible
>the universe

>>8371900
hahaha what the fuck r u on man