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The cantor expansion of a number may refer to several mathematical representation systems that are similar in principle:


 * Cantor expansion of integers, in which an integer $a$ is represented as $$\sum_{k=1}^na_k k!$$, where $$a_k\le k$$ are integers;
 * Cantor expansion of real number s, in which a real number $b$ is represented as $$b_0+\sum_{k=1}^n\frac{b_k}{k!}$$ ($n$ may or may not be finite) where $$b_0,b_1,b_2...$$ are integers with $$\forall k\ge 1,0\le b_k<k$$;
 * Generalizations of the above, mentioned below.

Cantor expansion of integers and generalizations
The cantor expansion of integers may be seen as a

Cantor expansion of real numbers and generalizations
(gen)