Prove the real numbers exist

Prove the real numbers exist.

Come on, Veeky Forums, you should be able to do this.

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stanford.edu/~jbooher/expos/ordinals_promys.pdf
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You can have a quantity of things that exist. This quantity of things exists in that quantity (duh). This quantity can be represented by a symbol arbitrarily, but that symbol always represents that quantity. Because that symbol represents a quantity of things that do exist, that symbol is said to be real. Repeat for any conceivable value.

Ergo, you're a faggot.

I'll disprove it:
NJ Wildberger has already done so.
QED

Define """real""".
Numbers do not exist in the first place

real in the maths sense I think is what he's asking. anything withouth an "i" componente (or j k l or whatever the fuck)

I can give whatever construction of the reals I like, and then you'll say something like
>dedekind cuts
>existing
>topkek famalam

Why bother?

1. peano
2. natural numbers
3. integers
4. rational
5. dedekind cuts muh suprasomethin
6. reals

If they don't exist, then how he know one when he doesn't see it?

Put that in your pipe and smoke it, constructivist!

Read the first chapter of Rudin's blue book

numbers do not exist .
you define them and thus create the idea of numbers .

If you attempt this kind of counterargument to burgerbrains out there they're going to refute it. They claim that burger has already disproven all these constructions (and other popular constructions of the reals) on his youtube playlist.

confining yourself to the rationals is perfectly valid, however be aware that you just voluntarily excluded yourself from 99% of modern mathematics.

I really cant believe that this guys goes pants on head when it comes to such simple things like sqrt(2), which has a very simple continued fraction representation, btw.

> continued fractions
> simple
I bet you believe in sine and the exponential function too.

>on his youtube playlist.

'Don't trust them, trust me. A guy who makes youtube videos.' -Jacksfilms 2012 when presenting a parody full of bullshit about the higgs boson.

>sci fell for the meme and burger can't stop laughing.

>starting with peano
>not magnitudes

This is why modern math is a joke.

Start with the greeks OP, and work your way forward. You'll realize most of modern "pure math" is actually not-so-thinly veiled applied math, pandering to either computer scientists (these days, most theory in math is almost exclusively at the service of cs and phys), chemists, astronomers, or all of the above. Mathematicians haven't done "pure math" since the greeks, who even then, were just the bitches of the astronomers.

Pure math is really just a myth. What you're doing isn't esoteric. Mathematicians only tell themselves that so they can sleep at night.

If you want to do real "pure math"- do it as a hobby.

Prove that they don't.

They seem like a useful idea to me. What insight do you get when you refuse to use real numbers? Are any theorems proven that couldn't be otherwise? Are any theorems more clear in derivation or generality? Does the introduction of the reals cause any contradiction?

Serious questions to prolly a bait thread.

He is the worst of both worlds. He actually begins his foundations of math videos while saying "w'ere not going to be using set theory or modern math" THEN LITERALLY constructs the naturals FIRST... (instead of talking about line segments and equal lengths, etc etc) WITH FUCKING PEANO'S AXIOMS. God I almost tore my fucking hair out. He combines the ignorance of people claiming there are only rational numbers, with the mindless obedience of the modern crowd who blindly accept what they're told and gobble up hilbert's program without questioning why they're doing it or what it's even for. Note, imo there are all tools to me. Whichever one works for what I need to be done is what I care about. I literally don't give a fuck about "muh universal truth". Non-constructive arguments are fun and all, but god fucking damn man. Fuck this guy.

Back to with you, degenerate humanities scum :^)

Do you have a video where he supposedly constructs the rationals from the naturals?
I'm curious how he does it without equivalence classes.

>I literally don't give a fuck about "muh universal truth".
Maybe because such a concept is absolutely fucking meaningless. It is useful for modeling reality or it is not. To argue anything else presumes that you yourself hold universal truth in your mind, which is batshit.

Agree with everything else. You can be interested in or disinterested in whatever the fuck you want, but don't cherry-pick to attempt to "prove" your "truth".

Constructive analysis is pretty cool. You can prove a lot of things.

wasn't there a mathematician that proved numbers and counting exists by first taking an empty set

Then putting that set in a set (1)
Then that set in another set (2)
Then in another set (3) and so on until it basically proved that you can count the sets and therefor numbers exist

????
you're talking about the construction of arbitrary finite numbers via ZF minus infinity

Hey man I dunno, I study chemistry

I just thought I read that somewhere

>I have 5 apples
>5 is the object we use to define the count of individual objects referred to as my apples
>no i don't because I assume I actually have the apples when in reality this is just a hypothetical

all of my what

You can't "prove" numbers exist. You can construct a bunch of things from axioms and call them numbers, which is probably what you're thinking of.

can't solve problems with the same thinking that creates them

I said he constructed the naturals from peano's axioms (uses a successor function to create strings of "ones"), and talked about "knowing" what size each number was in terms of "pairing" "elements" of the partitions of whole numbers with each other to see what is and isn't missing from the set to see which number was "bigger" or "smaller". He ended up using set theoretic descriptions while saying "I'm not going to use set theoretic descriptions".

your thinking of von neumann's construction

>stanford.edu/~jbooher/expos/ordinals_promys.pdf