# 1/Historical Note

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## 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. $580$ – $500$ 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