Playing with Infinity – Footnote 3

 

 

For the mathematically inclined, the number of ways that you can pick subsets of elements from a set containing n elements is 2ⁿ.  So, for instance, if the elements of a set are the numbers 1, 2 and 3, then you can pick eight subsets: 1, 2, 3, 12, 13, 23, 123 plus a subset containing nothing at all (the “empty set”).  Using the same pattern, we say that the size, or cardinality of the uncountable set aleph-one is the number two, raised to the power of aleph-nought.

 

 

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