Even bigger than infinity?


We can look at Hilbert’s hotel and other such problems, but to really understand the extent to which infinities reach, we need to know about a way of thinking called Set Theory.

A set is simply a collection of any objects or symbols, usually written inside curly brackets {} and separated by commas. For example, the set A might be written as “A = {1, 3, 5, 7}”

. We call the size of the set the cardinality, which is just the number of elements within the set. For A, the cardinality is 4. When two sets have the same ‘cardinality’, we can pair them, which is called a ‘bijection‘.

If we now think about an infinite set, for example, B = {1, 3, 5, 7, 9, 11…} or simply the natural numbers; N = (1, 2, 3, 4, 5, 6…}. The cardinality of this set is…

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