What is the practical purpose of incomprehensibly large numbers such as Aleph?
In: Mathematics
Aleph isn’t an “incomprehensibly large number”, it’s not a number at all, or at least not a number in the colloquial sense. Aleph is a [cardinal number](https://en.wikipedia.org/wiki/Cardinal_number), which is a something used to describe the size of infinite sets.
Infinite sets, as it turns out, can have different sizes. For example, the number of natural numbers (1,2,3,4,…) is the same as the number of integers (…,-3,-2,-1,0,1,2,3,…) and the number of rational numbers, but they’re all less than the number of real numbers. So in order to categorize these sets into groups of sets that all have the same size, we gave these sizes names, such as Aleph-null for the natural numbers and Aleph for the real numbers.
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