Palindrome (; "again") and ' (; "way, direction"). Palindromes date back at least to 79 AD, as a palindrome was found as a graffito at Herculaneum, a city buried by ash in that year. This palindrome, called the Sator Square, consists of a sentence written in Latin: "Sator Arepo Tenet Opera Rotas" ("The sower Arepo holds with effort the wheels"). It is remarkable for the fact that the first letters of each word form the first word, the second letters form the second word, and so forth. Hence, it can be arranged into a word square that reads in four different
Racetrack principle functions formula_23 and formula_24. Given that formula_1 for all formula_14, and formula_15, formula_28 for all formula_2, and formula_30, which by the proof of the racetrack principle above means formula_31 for all formula_2 so formula_4 for all formula_14. The racetrack principle can be used to prove a lemma necessary to show that the exponential function grows faster than any power function. The lemma required is that for all real x. This is obvious for x<0 but the racetrack principle is required for x>0. To see how it is used we consider the functions and Notice that f(0) = g(0) and that