Definition:Palindrome
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Definition
Definition 1
A palindrome is a string which stays the same when reversed.
Definition 2
A palindrome is a string defined as follows:
- $(1): \quad$ The null string $\epsilon$ is a palindrome.
- $(2): \quad$ If $a$ is a symbol, then the string $a$ is a palindrome.
- $(3): \quad$ If $a$ is a symbol and $x$ is a palindrome, then $axa$ is a palindrome.
- $(4): \quad$ Nothing is a palindrome unless it has been created by one of the rules $(1)$ to $(3)$.
Also see
- Results about palindromes can be found here.
Linguistic Note
The word palindrome derives from the Ancient Greek παλίνδρομος (palíndromos), meaning running back again.
This is formed from πάλιν (pálin), meaning back, again, and back again, and δρόμος (drómos), meaning running, race, and racecourse.