[ 3 / biz / cgl / ck / diy / fa / ic / jp / lit / sci / vr / vt ] [ index / top / reports ] [ become a patron ] [ status ]
2023-11: Warosu is now out of extended maintenance.

/sci/ - Science & Math

View post   
File: 29 KB, 445x100, 445px-Banach-Tarski_Paradox.svg.png [View same] [iqdb] [saucenao] [google]
[ERROR] No.3703078 [Reply] [Original]

So guys, lets see how much you know about the foundations of mathematics.
What would be the implication of the axioms of ZFC being proved consistant?

Also, lol at people who will inevitably call this a homework thread because they don't understand it.

>> No.3703112

Banach-Tarski paradox, a theorem about spheres and non-Lebesgue measurable things. Fun thing

>> No.3703119

>>3703112
It is. I meantion it at the start of my personal statement as an example of awesome mathematics that inspires my studying.
Unfortunately, my picture does not pertain to my question.

>> No.3703121

>>3703078

>What would be the implication of the axioms of ZFC being proved consistant?

I would fuck your mother, because a contradiction implies any proposition.

>> No.3703144

>>3703121
Contradiction also implies that you won't fuck my mother.
Check and mate.

>> No.3703150

>>3703144

What does it matter if I also won't fuck her?

The point is that I'll fuck her.

>> No.3703158

>What would be the implication of the axioms of ZFC being proved consistant?
It would imply ZFC isn't consistent.

>> No.3703176
File: 56 KB, 595x471, ahahaha.jpg [View same] [iqdb] [saucenao] [google]
[ERROR]

>>3703078

It would imply that ZFC is incomplete.

mfw stupid formalists think they can math.

>> No.3703179

>For any formal effectively generated theory T including basic arithmetical truths and also certain truths about formal provability, T includes a statement of its own consistency if and only if T is inconsistent.

Learn to Gödel

>> No.3703180

>>3703158
incomplete maybe?

>> No.3703195

>>3703180
>>3703176

ZFC is ALREADY incomplete because you CAN'T prove its consistency.

If you could prove its consistency, it would be complete but inconsistent.

>> No.3703218

>>3703195
Correct. If you prove that every axiom is consistant, then you've actually proven that it's inconsistant.
>>3703179
What do you mean 'Learn to Gödel'?
I wasn't looking for help - I was testing /sci/.

>> No.3703231

>>3703195
Except for the fact that ZFC hasn't been proven to be incomplete. To quote wikipedia "Nevertheless, it is unlikely that ZFC harbors an unsuspected contradiction; if ZFC were inconsistent, it is widely believed that that fact would have been uncovered by now. This much is certain — ZFC is immune to the classic paradoxes of naive set theory: Russell's paradox, the Burali-Forti paradox, and Cantor's paradox."

>> No.3703240

>>3703231

It hasn't been proven to be inconsistent. It's incomplete because it contains Peano Arithmetic as a subsystem.

>> No.3703298

>>3703240
>"we finally found a complete logical mathematical model!"
>"except we can't say whether or not arithmetic is logical"

>> No.3703303

This thread needs more Tarski's Undefinability Theorem and Loeb's theorem.