I guess that's fair, I'm being a bit sloppy. We prove things inside of axioms we accept, and can develop systems consistent with different sets of axioms but there's not necessarily any reason to choose one set over another. Doesn't 0^0 come from Euler being like "shut up it works nicer this way" though? or was it Russel?

We can't prove our axioms, and the rational number set isn't more true than anything else, it just tends to be more useful in normal arse problems.

[–] KnilAdlez@hexbear.net 6 points 1 year ago (1 children)

I can think of one reason to choose the set of axioms we all learned in grade school:

it just tends to be more useful in normal arse problems.

[–] naevaTheRat@lemmy.dbzer0.com 5 points 1 year ago

And anyone who's cared for a baby would tell you that lullabies are the most useful sort of music but they're hardly what I want to talk about when music comes up :P

[–] booty@hexbear.net 4 points 1 year ago (1 children)

Does everyone have to provide a disclaimer on every comment they ever make regarding math? (Note: This comment refers only to the system of mathematics every single person reading this comment is familiar with. If you make up different rules then those rules will apply instead of the ones I'm talking about.)

[–] naevaTheRat@lemmy.dbzer0.com 3 points 1 year ago

I didn't intend any hostility, the world is just nuanced and really fun. I often see assertions of rules of thumb presented as factual statements without any hint of further complexity existing and it makes me sad as people read that and think the world is simple and makes sense.

It's much more true to say something like "usually we can't divide by zero" and that leaves room for someone curious to go "huh!" and scurry off on their own and learn something fascinating.