I bet you can't prove that you can just chose an element from any set.

@PalteseMalconFunch Imagine having a set, a collection. Now you want to take one single element out of it, can you prove that you can always do that for every set? Intuitively, it's obvious but proving it formally, is something else.

@Luke73 Oh yea, I was just confused what you meant by “take out”.

Could you take out an element of the NULL set for example?

@PalteseMalconFunch What do you mean with NULL set? The empty set?

@Luke73 Yea, I learned is as NULL but I know like…0.1% of set theory 🤣

@PalteseMalconFunch I guess you're right, I forgot to mention that the set should not be empty. I'm not an expert on it either lol.

@Luke73 Ok so every set that contains at least one element. How would one even start to prove you can always remove an element? I have no idea.

@PalteseMalconFunch If you had a little of set theory, then you might have heard of the axiom of choice? That's basically what I'm describing. For countable sets and sets that contain a maximum or minimum value, that's not a problem but that's only a few special cases.

@Luke73 So how do you remove one element from an uncountable infinite set?

@PalteseMalconFunch I think I didn't phrase it exactly but it's not removing but rather choosing. Though removing one element isn't a problem. For example the set N\{5} where N is the set of Natural Numbers is the set without 5

@Luke73 OK sure I got you. So how do you choose the second element in an uncountable infinite set? You just use notation even though it doesn’t really make any sense?

@PalteseMalconFunch With countable numbers it's quite intuitive, like the Natural numbers. You choose the smallest number and then with the new set, you can choose the smallest again and through this process you're able to "extract" every number.

@Luke73 That’s what I’m asking. How do you even choose undefinable elements?

Or I guess it is definable? I dunno we’re way out of what I’m familiar with

@PalteseMalconFunch What do you mean with definable?