Definition:Finite Set Coding

Definition

Let $A \subset \N$ be a finite subset of the natural numbers.

Let $\ds n = \sum_{a \mathop \in A} 2^a$.

Then $n$ codes the finite set $A$, or $n$ is the code number for the finite set $A$.

Notes

This definition is arbitrary, and many other forms could replace it.

For example, any prime number could replace $2$ in the above definition.

Alternatively, $A$ could be ordered and coded as a finite sequence.

However, this particular definition has the convenient property that every natural number codes some finite set.

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