Anyone here who can give me some help about creating formula with these rules?
- $X$ is given to find $Y$
- $Y ≤ X$
- $Y$ cannot be equal $0$ -
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$f(x)=1$ if $x=1$, else $f(x)=x-1$. Satisfies all the properties except the contradiction between $y\lt x$ and $x=1$ implies $y=1$.
EDIT: Now that the question has been edited, this answer satisfies ALL the conditions. So, Ran, is this the kind of answer you want? or are there some other conditions you've forgotten to mention?