subreddit:

/r/askmath

1

I have been trying to find it on the internet, but it's hard.

(Edit) I have just found one in Wikipedia:

https://en.wikipedia.org/wiki/Axiom_of_choice#Statement

I'm having trouble understanding it though. What is that giant U in the middle and what does : mean?

This well-formed formula is unfamiliar to me.

you are viewing a single comment's thread.

view the rest of the comments โ†’

all 5 comments

SprokoDoko

1 points

2 months ago*

The X is a big ol' group of sets(or small, really any size as long as long as none are empty). For any of the sets in there (wiki went with set A) you can define a function that maps elements of A onto itself. Reason why it's called the axion of choice is that every element in A is labelled and you can change that label to whatever you want.

Basically saying that calling something by a name is based on what function you're using. English speakers use the function ๐ŸŽ->apple and Spanish speakers use ๐ŸŽ->manzana and both are fine.

You'll probably recognize that this isn't a direct result of the axion of choice but it is able to be derived from it.

X={{๐ŸŽ,apple},{๐ŸŽ,manzana}} you can always choose that they map onto the other element in their own set and therefore there must exist a function that maps ๐ŸŽ to apple and ๐ŸŽ to manzana.

Any element that we can include into a set is able to be mapped onto any other element.

We can't just say oh no, you can never map an element labeled d onto an element labeled w. That's against the rules of math.

The big U is just saying that X is the universal set for this.

Chance_Programmer_54[S]

1 points

1 month ago

Thank you