ITT we post quackery

WebTool
WebTool

ITT we post quackery

I'll start us off with the field of "Real" numbers, which is actually logically inconsistent with itself.

All urls found in this thread:
http://math.stackexchange.com/questions/472957/the-continuum-hypothesis-the-axiom-of-choice
RumChicken
RumChicken

the field of "Real" numbers is actually logically inconsistent with itself.
Yup, that's some gold-standard quackery right there.

VisualMaster
VisualMaster

@RumChicken
This

DeathDog
DeathDog

a number that does not exist

Top kek.

JunkTop
JunkTop

@RumChicken
@VisualMaster
The non-finitist quacks have arrived, everybody.

StrangeWizard
StrangeWizard

@WebTool
Since no one else is posting: The continuum hypothesis, which is less of an hypothesis and more of a conjecture by uneducated morons who refuse to work with other axioms than the ones their professors taught them decades ago.

5mileys
5mileys

which is actually logically inconsistent with itself.
Derive false from your favorite axiomatization of the reals of GTFO.

MPmaster
MPmaster

@WebTool
Real number are sequences of digits that are not rational.
Hows is this difficult to understand.

Brainlet.

Soft_member
Soft_member

Here's your reply, now get out.

Methshot
Methshot

@5mileys
0.999(9) = 1

SniperWish
SniperWish

@MPmaster
using a high school definition of reals
For shame

Soft_member
Soft_member

@MPmaster
"Real number are sequences of digits"
calls others brainlets

LuckyDusty
LuckyDusty

@WebTool
the only "real" numbers are the primes

whereismyname
whereismyname

@Methshot
Oh. But if you want it to be false you need unicity of decimal representation.
protip, there's no such a thing.

cum2soon
cum2soon

@whereismyname
So basically Dewey created one of the dankest memes

5mileys
5mileys

@Methshot
Reals axioms don't require real numbers to have unique decimal representation

Dreamworx
Dreamworx

@MPmaster
The real numbers contain the rationals
even the people hating on this post haven't pointed that out
holy shit this is why i use physicsforums

Raving_Cute
Raving_Cute

@WebTool

Be real OP, this is just a contrived way of making a 0.999... = 1 thread

TurtleCat
TurtleCat

@MPmaster
Given that you want the real numbers to be a field, with a unique identity (1) and so on, you'd really have to consider an equivalence class of sequences (where e.g. the set {[0,9,9,...] and [1,0,0,...]} models the number "1") and so this isn't much better than the Cauchy sequences.
Cauchy sequences are probably chosen over "equivalence classes of sequences of digits" because it lends itself better to analysis (calculus).

Nojokur
Nojokur

@StrangeWizard
Is you best argument against the CH is that "its not a hypothesis its a conjecture"?

That's nitpicking. It's doubtful you even understand people's complaints about it.

Watching Wildberger does not mean you have an educated opinion on mathematical logic or set theory.

Dreamworx
Dreamworx

@Dreamworx
There's just so much wrong with it, its hard to know where to start.

Need_TLC
Need_TLC

@MPmaster
top lel

CouchChiller
CouchChiller

@Nojokur
Is you best argument against the CH is that "its not a hypothesis its a conjecture"?
My best argument against CH is that any reasonable axioms you choose to perform set theoretical work in should make it possible to prove it false.

FastChef
FastChef

@CouchChiller
so a reasonable axiom system for you includes the negation of CH?

JunkTop
JunkTop

@CouchChiller
Real analysis doesn't like CH that much.

Ignoramus
Ignoramus

@FastChef
It doesn't necessarily have to include CH's negation, just imply it.

Spazyfool
Spazyfool

@JunkTop
does real analysis even care about CH?
the only axiom I've really seen being discussed in a real analysis context is AOC.
@Ignoramus
what axiom would you suggest that implies it's negation?

King_Martha
King_Martha

@Spazyfool
AOC implies the law of excluded middle

CouchChiller
CouchChiller

@Spazyfool
what axiom would you suggest that implies it's negation?
That's not my point. I don't propose any axiom, I just refuse to accept axioms that don't imply CH's negation.

Emberburn
Emberburn

@CouchChiller
I think you mean "I refuse to accept axioms that imply CH"

You don't want to bar the possibility of accepting axioms which are independent of CH ;)

Stupidasole
Stupidasole

@Emberburn
I think Godel proved that CH can't be proved with the current axioms. If I remember right, there are proofs in real analysis that prove the axiom of choice, but CH implies AOC. Do you see the contradiction?

Fried_Sushi
Fried_Sushi

@Stupidasole
I think Godel proved that CH can't be proved with the current axioms.

Actually that it's independent of the ZFC axioms. You can't prove OR DISPROVE the CH with just the ZFC axioms (which includes choice). What you remember is not correct.

takes2long
takes2long

@WebTool
which is actually logically inconsistent with itself
go on. you asserted a claim. prove it.

Supergrass
Supergrass

@Fried_Sushi

The ZFC universe is a large one. If you can't prove it in ZFC + the Grothendieck add-on, I don't see how AOC can be proved so easily in real analysis. Even though it has been a while, I think they had us "prove" AOC with the well-ordering principle or some shit like that. I'm just saying AOC is a spin-off of CH, and the CH is undecidable. That's the contradiction. AOC is also undecidable.

Carnalpleasure
Carnalpleasure

@Supergrass
http://math.stackexchange.com/questions/472957/the-continuum-hypothesis-the-axiom-of-choice

Continuum hypotesis doesn't imply AoC but Generalised CH implies AoC, which can Be proved in ZF.

Snarelure
Snarelure

@WebTool
ITT we post quackery

Oops.

SniperGod
SniperGod

@Carnalpleasure
Do you know what undecidable means?

viagrandad
viagrandad

@Stupidasole
there are proofs in real analysis that prove the axiom of choice
No.
CH implies AOC
No.
Please actually learn the subjects you're talking about before shitposting on Veeky Forums.

Bidwell
Bidwell

@viagrandad
Sorry user, I don't think you know what you're talking about.
carry on

FastChef
FastChef

@SniperGod
Whoops I meant assuming GCH, it implies AoC

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