[DerpObvious]

You have to remember what we mean by 'size': there are four things in the set {ball, kite, hat, glove} because we can line them up one-to-one with {1, 2, 3, 4}. For an infinite set, they're the same 'size' if we can line up everything in one set with everything in the other.

For a bigger circle and a smaller circle, consider lines through their mutual center (if you line them up concentrically). You can take a ray from the center out to the first circle, and then out to the second circle, and this will line up all the points exactly one-to-one between the two circles. There are no points on the outer circle which don't get hit by some ray, so it can't be 'bigger'.

For the set [1, 2] versus [1, 10], you just use the function f(x) = 9 * (x - 1) + 1 to map everything from the first set to the second. There's nothing in [1, 10] that f doesn't map to, so it can't be 'bigger'.

What's really interesting is that there are as many even integers as integers at all - you just multiply everything by two, and you line them up one-to-one!

(Hint: the definition of being infinite is that you have a proper subset of yourself that's the same 'size'. That's why we get this weird behavior... infinity is nothing like the counting numbers we're used to!)