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I define a function from positive integers to positive integers as follows. First, write the number in decimal notation. Then, reverse the digits and delete any leading zeros, if any leading zeros are there. Then, the number you get is the output of the function. I denote this function by $\operatorname{rev}(x)$. For example, $\operatorname{rev}(2)=2$, $\operatorname{rev}(10)=1$, and $\operatorname{rev}(120)=21$. Does the function $\operatorname{rev}$ satisfy the functional equation $\operatorname{rev}(x)=\operatorname{rev}(\operatorname{rev}(\operatorname{rev}(x)))$?

Bill Dubuque
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user107952
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    Yes because once the zeros are removed you're merely reversing the string. – CyclotomicField Mar 20 '21 at 16:01
  • Special case $x=10$ of the polynomial generalization in the linked dupe: i.e. once you reverse a polynomial $f,$ the result $,r(f),$ has no trailing zeroes, so its reverse has the same degree, so, as proved there, reversing $,r(f),$ twice is the identity operation, i.e. $\ r^2(r(f)) = r(f)\ \ $ – Bill Dubuque Mar 20 '21 at 16:56

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