1/Historical Note

Historical Note on $1$ (one)

The ancient Greeks did not consider $1$ to be a number.

According to the Pythagoreans, the number One ($1$) was the Generator of all Numbers: the omnipotent One.

It represented reason, for reason could generate only $1$ self-evident body of truth.


While a number, according to Euclid, was an aggregate of units, a unit was not considered to be an aggregate of itself.

The much-quoted statement of Jakob Köbel might as well be repeated here:

Wherefrom thou understandest that $1$ is no number but it is a generatrix beginning and foundation for all other numbers.
-- $1537$

illustrating that this mindset still held sway as late as the $16$th century.


The ancient Greeks considered $1$ as both odd and even by fallacious reasoning.


Sources

  • 1969: Karl Menninger: Number Words and Number Symbols
  • 1980: David M. Burton: Elementary Number Theory (revised ed.) ... (previous) ... (next): Chapter $1$: Some Preliminary Considerations: $1.3$ Early Number Theory
  • 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $1$
  • 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.2$: Pythagoras (ca. $\text {580}$ – $\text {500}$ B.C.)
  • 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $1$
  • 2008: Ian Stewart: Taming the Infinite ... (previous) ... (next): Chapter $2$: The Logic of Shape: Pythagoras
This article is issued from ProofWiki. The text is available under Creative Commons Attribution-ShareAlike License unless otherwise noted. Additional terms may apply for the media files.