Is 0 the smallest whole number

Zero is a whole number if you are referring to the non-negative integers, or all integers.

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, ...).

However there is another opinion:

0 (called "zero" or "nil") means "nothing exists" so 0 cannot be a real number at all.

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.

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 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.

Is there anything proven which actually contradicts the "mathematical hypothesis about the smallest number" which is summarized by those last four statements?