07-29-2021, 10:01 AM

Now I have a proof of only one infinity! Well, sort of. Because infinities can't be added. For example adding 1 to infinity doesn't make sense and is an invalid operation since it mixes apples and oranges (infinity and a number). And adding infinity to infinity is invalid since infinity is not a number. And using the Axiom of Choice is invalid since it can only select one element from each set (if I understand it correctly). It's impossible to make an infinite number of choices needed for addition of infinities (when would such choice-making process be completed?).

But can't there be different "sizes" of infinities as in math? That's based on the assumption that sets such as the natural numbers can be treated as completed infinities. That's a fallacy since there is no largest number, hence the definition becomes invalid, and the same for all other endless sets like that.

I'm not entirely sure I'm correct about that, haha, but I wanted to post it as something to explore further.

But can't there be different "sizes" of infinities as in math? That's based on the assumption that sets such as the natural numbers can be treated as completed infinities. That's a fallacy since there is no largest number, hence the definition becomes invalid, and the same for all other endless sets like that.

I'm not entirely sure I'm correct about that, haha, but I wanted to post it as something to explore further.