1/Historical Note

Historical Note on 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.

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 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.