User:Triakula/Reversing operator

Let's define operator \(\sigma\) like so:

If natural number \(N\) is in the form \(d_1 d_2 \cdots d_n\) where \(d_i\) are decimal digits, then \(\sigma N = 0. d_n \cdots d_2 d_1 000 \cdots\).

Hypothesis:

\(\forall N \in \mathbb N \exist \sigma N | \sigma N \in \mathbb R\)