I mean, Cantor said so, not I. But an easy example
Imagine a list of all whole numbers. 1, 2, 3 on up and up. Obviously this list is infinite - numbers do not end.
Now imagine a list of all real numbers - that is, all numbers plus their decimal amounts between each while number. 1, 1.1, 1.11, 1.12, 2, 2.1, and so on. This list is also infinite - but it is also inherently larger than the infinite list of only whole numbers. It has more numbers.
That’s like saying am infinite number of feathers is lighter than an infinite number of bricks. Neither is heavier than the other - they’re both infinitely heavy.
You’re measuring a quality of the two objects, not the quantity, which might make a difference. I’m just sharing something I learned that I think is cool:)
I mean, Cantor said so, not I. But an easy example
Imagine a list of all whole numbers. 1, 2, 3 on up and up. Obviously this list is infinite - numbers do not end.
Now imagine a list of all real numbers - that is, all numbers plus their decimal amounts between each while number. 1, 1.1, 1.11, 1.12, 2, 2.1, and so on. This list is also infinite - but it is also inherently larger than the infinite list of only whole numbers. It has more numbers.
That’s like saying am infinite number of feathers is lighter than an infinite number of bricks. Neither is heavier than the other - they’re both infinitely heavy.
You’re measuring a quality of the two objects, not the quantity, which might make a difference. I’m just sharing something I learned that I think is cool:)