/sci/ - Science & Math

[Anonymous No.10667809]

"Banach Tarski" is an anagram of "Banach Tarski Banach Tarski"

[Anonymous No.10667876]

>>10667809
Trop de ski tue le ski.

[Anonymous No.10667889]

[Anonymous No.10668130]

Based

[Anonymous No.10668133]

HMMMMMMMMMMMM

[Anonymous No.10668181]

>>10667809
Haha my joy is non-measurable

[Anonymous No.10668189]

>he believes axiom of choice

[Anonymous No.10668199]

>>10668189
>he believes axiom of choice
I'm not a "he".

[Anonymous No.10668200]

>>10668199
please delete

[Anonymous No.10668221]

>>10668181
Haha

But is there any actual application to the AoC? It seems like every time it's used you could just replace your statement with a slightly more discriptive one and not loose anything, like instead of saying all vector spaces, say all vector spaces with a basis. What's an example of a vector space with no basis that's ever used even in the purest of math?

[Anonymous No.10668252]

>>10668221
>What's an example of a vector space with no basis that's ever used even in the purest of math?

You mean a space we cannot explicitly write down a basis without appealing to axiom of choice? I don't know, can you write down explicitly a basis for C([0,1])?

[Anonymous No.10668267]

>>10668221
>It seems like every time it's used you could just replace your statement with a slightly more discriptive one and not loose anything
We can’t do this all the time. Famous example: if S contains all non-empty subsets of the real line, no explicit choice from S exists and we can only assume its existence as an axiom.
So basically in every proof where choice function seems to be impossible to construct just use AoC.

[Anonymous No.10668307]

>>10668221
Without axiom of choice D-finite and finite are not the same conditions.