ROADWAYS & HORIZONTALS


THE PEANO POSTULATES
The Laws of Sequence


1. Zero is a number.
2. Every number n has exactly one successor n'.
3. Zero is not the successor of any number.
4. No two numbers have the same successor.
5. If n belonging to a set of numbers called S implies that its successor n' also belongs to S, and if 0 is also in S, then S contains all the numbers.
-GIUSEPPE PEANO
Formulaire de Mathématiques (1889)

Any progression may be taken as the basis of pure mathematics: we give the name 0 to its first term, the name number to the whole set of its terms, and the name successor to the next in the progression. The progression need not be composed of numbers: it may be composed of points in space, or moments of time, or any other terms of which there is an infinite supply. Each different progression will give rise to a different interpretation of all the propositions of traditional pure mathematics; all these possible interpretations will be equally true.
-BERTRAND RUSSELL
Introduction to Mathematical Philosophy (1919)

"Well now, would you like to hear of a race-course, that most people fancy they can get to the end of in two or three steps, while it really consists of an infinite number of distances, each one longer than the previous one?"
LEWIS CARROLL
What the Tortoise Said to Achilles (1895)

He sat leaning on his cane and thinking that with a Knight's move of this lime tree standing on a sunlit slope one could take that telegraph pole over there, and simultaneously he tried to remember what exactly he had just been talking about.
-VLADIMIR NABOKOV
The Defense (1964)


-W. A. MOZART
Symphony 40 in G minor: Movement I (1788)

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