In reply to:

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The set of all subsets of a given set has a larger cardinal number than the set itself, resulting in an infinite succession of cardinal numbers of increasing size.

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Er, well, you'd think so, but not necessarily. For instance, you'd think that a two-dimensional grid of integer coordinates would logically have to be a larger infinity than the infinity of integers. But not so. To prove this, start with the origin, Then, draw a line up to (0,1) and proceeding clockwise to (1,1), (1,0), (1,-1), (0,-1), (-1,-1), (-1,0) and (-1,1). The move one circuit outwards and so forth. Eventually you will form a line - the spiral - which includes all of those points. Thus, the two-dimensional grid is exactly the same order of infinitude (ie. same Aleph number) as the set of integers.

Enumerating infinities does strange things to the consciousness of humans.

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