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Anonymous at Thu, 11 Apr 2024 06:50:26 UTC No. 16123699
If there are an infinite number of whole numbers, and an infinite number of decimals between any two whole numbers, and an infinite number of decimals in between any two decimals, does that mean that there are infinite infinities? And an infinite number of those infinities? And an infinite number of those infinities? And an infinite number of those infinities? And an infinite number of those infinities? And… (Infinitely times. And that infinitely times. And..) …
Anonymous at Thu, 11 Apr 2024 08:48:20 UTC No. 16123808
>>16123699
You're partially right.
There is the same 'number' (cardinality of the set) of whole numbers as finite-length decimals and rational numbers. But there is a higher order of infinity beyond that, for all decimal numbers, including irrational ones.
As a simple example, the number of points in a line of 1 cm length is infinite. The number of points in a line of 2 cm length is also infinite, even though this line is twice as long as the first. For every point in line 1, there is a corresponding point in line 2.
https://en.wikipedia.org/wiki/Aleph