Definition:Palindrome

From ProofWiki
Jump to navigation Jump to search

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.