# Creating Formula for a function $Y$ = $f(X)$ satisfying some conditions [closed]

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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## closed as not a real question by mixedmath♦, Qiaochu YuanAug 29 '11 at 18:46

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You state that if X = 1, then Y = 1, but you also state that Y must be less than X. Isn't this impossible, since 1 is not less than 1? –  Tanner Swett Aug 22 '11 at 2:30
What is the domain (i.e., what values is $X$ allowed to take)? –  Arturo Magidin Aug 22 '11 at 2:32
You have not stated, but probably are thinking, that the function should be continuous. Then $y \ne 0$ means that $y$ is always the same side of $0$. If $y \gt 0$ you must have $x \gt 0$. I suspect Gerry Myerson's solution is not what you are thinking, but explaining why may help the definition. –  Ross Millikan Aug 22 '11 at 4:47
@Ross, I also suspect my solution is not what Ran has in mind, but I'm hoping it will stimulate Ran to clarify. –  Gerry Myerson Aug 22 '11 at 7:32
it can be y <= x.. –  Ran Gualberto Aug 22 '11 at 10:14

$f(x)=1$ if $x=1$, else $f(x)=x-1$. Satisfies all the properties except the contradiction between $y\lt x$ and $x=1$ implies $y=1$.