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What's the difference between countable and uncountable infinity
- Thread starter Deonment
- Start date
- 9,626
- 10,333
Countable: For example all natural numbers (1,2,3,4,5....ad infinitum), infinites you can theoriticaly count up to, given a infinite amount of time.
Uncountable: For example all real numbers (Just google what real numbers are). Infinites so big that even if given infinite amount of time you woudnt be able to count up to them.
One of the easiest example is from Vsauce. He compared natural numbers with real numbers, pointing out that real numbers can have literal infinites between 0 to 1. With natural numbers, you go from 0 to 1. With real numbers, the next biggest number is 0.000000000000(ad-infinitum)1, the next biggest number on that would be 0.0000000000(ad-infinitum)2 and so on. In this example, you would have an entire infinity between each number.
Uncountable: For example all real numbers (Just google what real numbers are). Infinites so big that even if given infinite amount of time you woudnt be able to count up to them.
One of the easiest example is from Vsauce. He compared natural numbers with real numbers, pointing out that real numbers can have literal infinites between 0 to 1. With natural numbers, you go from 0 to 1. With real numbers, the next biggest number is 0.000000000000(ad-infinitum)1, the next biggest number on that would be 0.0000000000(ad-infinitum)2 and so on. In this example, you would have an entire infinity between each number.
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