*(Notice: Due to recent health problems it has been difficult for me to continue with my blog. I still intend to write future posts as I am able, while also working on my new book series in the background. As a sign of good faith here is an excerpt from the first volume.)*

A palindrome is defined in this essay to be any finite sequence $(a_1, a_2, \ ... \ , a_n)$ such that

\[ (a_1, a_2, \ ... \ , a_n) = (a_n, a_{n-1}, \ ... \ , a_1) \ . \]

It is assumed that every element of the palindrome belongs to some finite set of elements $A$. This can be thought of abstractly as the set of letters in a given alphabet, or we can also think of it as the set of symbols in a given integer base.