Can you really fit ALL the counting numbers into the spaces between 0 and 1?
Two trails can both keep going out of sight. Pairing and listing give us a fair way to ask whether those two kinds of forever are really the same size.
Talk about it
- Guess first: are there more counting numbers or more even numbers? Then try pairing them 1→2, 2→4, 3→6 and see what happens.
- If someone promised you a list with every decimal on it, how would you prove one was missing?
- What do you think 'a bigger infinity' means if both piles still go on forever?