Numbers parity

Any number, except zero, multiplied twice, is an even number.
A pair has two elements.

Demonstration:

One multiplied twice, result is a pair.
A pair has two elements.

Two multiplied twice, result is two pairs.

Zero exception:

Zero multiplied twice, resulting zero pairs.
Zero pair has zero elements, therefore:

The number zero is neither odd nor even.

Conclusion:

The smallest odd number is one.
The lowest even number is two.
The number zero is neither odd nor even.


The classic definition:

necessary condition,
(NOT SUFFICIENT CONDITION,)
to determine whether a number is even,
to be divisible by two.


Bibliography:


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