Is zero a natural number?

[polymath257]

Great explanation, Poly, even though I am siding with most anthropologists on this likely insignificant question.

If you go to the ancient Greeks, 1 wasn't considered a number either.

[Jack8]

Yes. Anywhere from minus Infinity to positive Infinity is natural including 0.

[UniversesBoss]

Yes it is.

[Jehanne]

Two banned users times 0 is still 0 users.

[LinuxGal]

Zero does not have any positive or negative value so zero cannot be a natural number. But it sure is a whole number

It's a whole lot of nothing, maybe.

[Angrboda]

Nothing is better than a ham sandwich. Nothing. Except maybe a nice MLT -- a mutton, lettuce, and tomato sandwich, where the mutton is nice and lean and the tomatoes are ripe. They're so perky. I love that.

[rocinantexyz]

Yes. Anywhere from minus Infinity to positive Infinity is natural including 0.

I've seen zero included and excluded by slightly different definitions. Until now I've never seen anyone try to smuggle in all of the integers.

[Carl Hickey]

Hi,

Let's take a set of apples.

The set is full. If there were no apples the the set would be empty.

Full set and empty set are complementary.

Let's state that a quality of a full set is a Natural number.

- - -

An unoriented line segment (1 d) is a set of units (Greeks, rational numbers (set (of sets (of ...))).
Rational numbers are natural numbers. Greeks discovered irrational numbers (square root of 2).
Irrational numbers are not natural numbers (not expressed as set (of sets)).

= = =

empty (zero)

full:
- unoriented (0 d, set (natural number))

- oriented line segment (1 d, vector);

- oriented piece of plane (2 d, bi-vector);

- oriented volume (3 d, ...);

- ...

= = =

...

[Carl Hickey]

Great explanation, Poly, even though I am siding with most anthropologists on this likely insignificant question.

If you go to the ancient Greeks, 1 wasn't considered a number either.

Hi,

An apple is a thing (unit). Quality of an apple: red, sweet, hard, ...

A full set of apples (1 apple (the apple is the unit)): the set is a thing; the quality of the set is 1.

[Carl Hickey]

...

= = =

Lateral (complex) numbers: oriented line segment (vector, 1 d) in a plane (2 d).

a (length, angle), b (length, angle)

c = a . b (length (a) . length (b), angle (a) + angle (b))

-

(-2) . (-3) = 6 (2 . 3, pi/180 + pi/180 = 2 pi/360/0)

i (1, 90)

i . i = -1 (1 . 1, 90 + 90 = 180)

= = =

Natural numbers were created by God, everything else is the work of men.
Kronecker (1823–1891).

= = =

In the beginning was the Word, and the Word was with God, and the Word was God. He was with God in the beginning. Through Him all things were made, and without Him nothing was made that has been made. In Him was life, and that life was the light of men. The Light shines in the darkness, and the darkness has not overcome it.

...
/word ~ logos ~ wisdom ~ .../

Gospel of John