I bet you can't prove that 0 is the smallest natural number.

Try it, you can't.

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Quite right. In fact, I can prove that 0 is not the smallest natural number: the natural set begins at 1, so 0 isn't even a natural number

Luke73 · 26-30, M

@ImperialAerosolKidFromEP It depends on your definition, 0 as the smallest natural number is as valid as 1 is.

ImperialAerosolKidFromEP · 51-55, M

@Luke73 Well then, according to my definition, 3.14 is a natural number. But the formal definition I was given as far back as high school excludes 0 (3.14 as well)

Luke73 · 26-30, M

@ImperialAerosolKidFromEP Conventionally in mathematics, you have the natural numbers and the natural numbers with zero.

ImperialAerosolKidFromEP · 51-55, M

@Luke73 If we define them as we fancy. If we're going by the formal definition, whole numbers include 0 (ℕ₀)

Luke73 · 26-30, M

@ImperialAerosolKidFromEP ℕ₀ is natural numbers including zero. Whole numbers is an ambiguous term.