ELI5: There are infinite numbers between 0 and 1. There are also infinite numbers between 0 and 2. There would more numbers between 0 and 2. How can a set of infinite numbers be bigger than another infinite set?

Because having more of something is (in general) unrelated to your ability to count it.

You "have more" if after pairing things up there are still leftovers. One way to pair things up is to count, but that's certainly not the only way.

I don't have an actual five year old, but if I did, I would try this: take unequal bunches of red and blue poker chips and put in a bag. They can only take 2 chips out at a time. They can mark the chips (with a single black mark, not with a number) but then need to put them back in the bag. How can they tell if there are more red or blue poker chips? One strategy is to mark both chips only if you pull out an unmarked blue and unmarked red. Repeat and eventually the only unmarked chips you will find is from the larger set.

/r/explainlikeimfive Thread