Are negative numbers and the number zero whole numbers?

Answer 1

0 (called "zero" or "nil") means "nothing exists" so 0 cannot ever be a real number, no matter whether we are considering positive or negative numbers.

So the smallest whole number is 1, also known as "one" or "unity".

Because it is the "magnitude" or "size" of the number which is being asked about in this kind of question - and not its "polarity" or "sign" - the previous sentence remains true no matter whether we are considering positive or negative whole numbers.

Another opinion

The term 'whole number' does not have a consistent definition. Various authors use it in one of the following senses:

• the non-negative integers (0, 1, 2, 3, ...)
• the positive integers (1, 2, 3, ...)
• all integers (..., -3, -2, -1, 0, 1, 2, 3, ...).

Yet another opinion

Here are some relevant mathematical statements:

• 1 (One) is the smallest number.
• Any expression that computes to a value which is less than 1, no matter how small, is always just a label stating a mathematical expression such as 1/3, 0.3333(recurring), 1/1000, 0.001, 1/(zillions of zillions), etc. and that expression must, by definition, always relate back to the smallest whole number, which is 1.
• The number 0 ("zero" or "nil") is always just a plain label, worth nothing because it has no magnitude, which was invented as a label specifically to be able to state: "There is no number having any value or magnitude present in this place."
• Because zero is always worth nothing because it has no magnitude, it is always JUST a symbol, a plain label, etc., so it can be neither a "whole" number nor a "small" number nor the "smallest" number.

Those last four statements form a mathematical hypothesis - also known as a scientific theory or conjecture - about the smallest number that remains open to be disproved but so far has never been disproven.

Does anyone know anything more?