TIL that there are differently sized infinities. In 1873, mathematician Georg Cantor proved that the size of the infinite set of fractions is the same size as the counting numbers (1, 2, 3, 4,…); he later proved the surprising result that not all sizes of infinities are equal.

Read more: https://www.britannica.com/science/infinity-mathematics

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  1. It kind of just makes sense. There are an infinite number of whole numbers and there are an infinite number of even numbers, but logically the infinite set of evens must be smaller than the infinite set of whole numbers.

  2. This should be intuitive as well. If you take all the numbers (odd, even, algebraic, etc) and did a 1:1 with all of the numbers between 0 and 1….there is an infinity between 0 and 1 that is larger than the infinity of any ordered list

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