Could anyone tell me what this transformation looks like?
$T: [0,1)\to [0,1), T(x)= 10x\quad (\text{mod} \quad 1)$
If $x=0.31$ then $T(x)=3.1$, now modulo $1$ means what? Thank you.
2026-04-02 20:09:00.1775160540
What it means by Modulo $1$ in a self-transformation
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It is a way of saying "Take the decimal part". Clearly multiplying by $10$ easily brings you out of the interval $[0,1)$, so this solves the problem. In this way $T(0.31)=0.1$.
A correct way of writing that should be: $$T(x)=10x-\lfloor 10x \rfloor \ .$$ In your case you would have: $T(0.31) = 3.1-3=0.1$ .