Comments by "eggynack" (@eggynack) on "TED-Ed" channel.

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  30. You kinda missed the point of a lot of what I said. To your first claim, do you agree that 1+1=2? If so, then proving that infinity+1=infinity would be sufficient to show that infinity is special in this regard. So, we'll start with the set of all positive integers, here assumed not to include zero. Then, we will compare it to the union of the set of positive integers with zero. To prove these sets have the same size, we need merely construct a mapping from one set to the other. The mapping in question will be to take each element from the positive integers plus zero and add one to it to get an element of the set of positive integers. So, 0 maps to 1, 1 maps to 2, 2 maps to 3, and so on. In this fashion, every single element from the first set is paired with exactly one element from the second set. However, the second set is the first set with one additional element, so we have taken the first infinity, added one to it, and reached an infinity of the same exact size. To your second claim, I think you've just straight up misread me. I didn't say that infinity is a number. I said that, whether infinity is a number or not, we can add to it. If your definition of number doesn't include infinity, then, well, I guess there's just another type of thing we can reasonably add numbers to. Who cares about the word "number" anyway? To the third, again, I have literally no idea where you're getting the idea that that's what I said. The hotel is not full with no one in the first room. What I said was that you can put infinite guests into the hotel and not necessarily fill it. You referred to putting infinite guests into the infinite hotel as subtracting infinity from infinity, but my point was that this subtraction has a ridiculous variety of results. You can take the same exact quantity of guests and reach a ton of different levels of hotel fullness.
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