How It Started, How It's Going
A bijection between the integers and the natural numbers shows ℤ, despite containing ℕ plus infinitely many more, isn't any bigger.
Use this cartoon
Free for classrooms, worksheets, slides and other non-commercial use under CC BY-NC 4.0, with credit to Ben Orlin.
Cartoon by Ben Orlin, Math with Bad Drawings. https://cartoons.mathwithbaddrawings.com/2024-01-01-how-it-started-how-it-s-going/ (CC BY-NC 4.0)Transcript
[How It Started] 0, 1, −1, 2, −2, 3, −3, 4, −4, … mapped by arrows to 1, 2, 3, 4, 5, 6, 7, 8, 9, …
[How It's Going] ℤ: "I have all the numbers you do, right?" ℕ: "Yup, every one." ℤ: "And I have other numbers, too?" ℕ: "Oh yes, infinitely many others." ℤ: "So… I have more numbers, right?" ℕ: "Ha! No."