What is the practical purpose of incomprehensibly large numbers such as Aleph?
In: Mathematics
Love the replies so far. Just wanted to add one thing.
There is a lot of use to extremely large numbers, one application being encryption. Extremely large prime numbers are used to encrypt data because they are exceptionally hard to calculate and provide a great way to easily encrypt data quickly and securely.
Then there are *absurdly large* numbers. I’m talking about numbers with billions of digits. These serve almost no practical value to us. Occasionally we will discover a number with a cool property, but beyond that the number exists as a footnote on the OEIS (Online Encyclopedia of Integer Sequences).
They aren’t really numbers, nor do they have any practical value. They are discussed since they reveal interesting properties about the structure of the mathematical universe.
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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