> 2 green apples plus 2 red apples equals 4 apples
What a load of malarkey. This statement is not a problem for traditional mathematics. I have 2 green apples and 2 red apples right here in my bag (eh, set), and the size of the set is 4, and all elements of the set are apples, some of them are red, some are green. What is the problem? I can tell you: type theory.
> I have 2 green apples and 2 red apples right here in my bag (eh, set), and the size of the set is 4, and all elements of the set are apples, some of them are red, some are green.
Well, is your set equal to a set of 3 green apples and 1 red apple, or not? (And actually how can you have multiple green apples in the same set if they're equal?)
Just because two apples are both green doesn't mean that they are equal. In fact, if there are two apples, that means they are definitely not equal, otherwise there would be just one green apple. No, the set is not equal to a set of 3 green apples and 1 red apple, under the assumption that a green apple cannot be a red apple (and vice versa). Any more questions?
> Just because two apples are both green doesn't mean that they are equal. In fact, if there are two apples, that means they are definitely not equal, otherwise there would be just one green apple.
Well, a green apple had better be equal to itself. So if you've got a green apple and another green apple that isn't equal to the first, you're already in trouble and going to have to resort to hacks like numbering them.
> No, the set is not equal to a set of 3 green apples and 1 red apple, under the assumption that a green apple cannot be a red apple (and vice versa).
What if you want to manipulate it in a context where you only care about the number of apples, not their colour?
> Well, a green apple had better be equal to itself. So if you've got a green apple and another green apple that isn't equal to the first, you're already in trouble and going to have to resort to hacks like numbering them.
Nope, no trouble at all. Those troubles only exist in your type-infested mind.
> What if you want to manipulate it in a context where you only care about the number of apples, not their colour?
Then I'll do just that. Lol, you can't make this shit up.
What a load of malarkey. This statement is not a problem for traditional mathematics. I have 2 green apples and 2 red apples right here in my bag (eh, set), and the size of the set is 4, and all elements of the set are apples, some of them are red, some are green. What is the problem? I can tell you: type theory.