The title is a bit absurd, we could examine the distance of any number from itself..

In the previous post I examined the property of distance being even or uneven. Let’s go back to distance of zero from itself. Formally the distance of zero from itself is |0 – 0| = 0. 0 mod 2 = 0, why isn’t this distance even?

The distance doesn’t exist, instead of distance we have a point. Euclid’s definition to a point is: “A point is that which has no part.” In Euclid words the “distance” of zero from itself, |0 – 0| = 0 has no part. Something like this isn’t even or uneven.

In an e-book called “The Way To Geometry” it says, that magnitude of a point is zero.

Philosophically speaking a point is what Democritus called “atomos” applied to geometry.

In short, there isn’t distance of zero from itself. The meaning of distance |0 – 0| = 0 is geometrically a point, something that has no part.

The main point is, that I see zero as a neutral number. What does that mean?

- Zero isn’t even or uneven
- Zero isn’t negative or positive
- Zero doesn’t have numerical opposite

*The meaning of the video clip: “..achievements: Zero.”
*

*Probably zero is my greatest*

*achievement too…*🙂

Semantically zero is *none*, not nothing.

In multiplication zero overrides the neutral element property of one: 1 * *a *= *a*, but if *a *= 0, zero “zeroes” one. The number one doesn’t keep the identity of zero, but zero “zeroes” number 1’s neutral element property and keeps the identity of its own.

Let us examine the even and uneven property of zero from point of view of distances.

The distance of number 2 from zero is |0 – 2|= 2. 2 mod 2 = 0; 2 is even.

The distance of number 3 from zero is |0 – 3|= 3. 3 mod 2 = 1; 3 is uneven.

The distance of number 4 from zero is |0 – 4|= 4. 4 mod 2 = 0; 4 is even.

But what about our friend zero?

The distance of number zero from itself is |0 – 0| = 0. 0 mod 2 = 0, but now the meaning of zero is, that the distance doesn’t exist. There isn’t distance from zero to zero. The distance that doesn’t exist isn’t even or uneven. Therefore now zero can’t be considered even or uneven.

In multiplying one (1) is neutral element: *a ** 1 = *a. *For example, 7 * 1 = 7. Number one keeps the identity of a number, which includes a number being even or uneven. But what about zero (0)?

0 * 1 = 0. Does one keep the identity of zero or does zero keep the identity of its own? The property of this identity is ”zeroing” property: *a * *0 = 0, were *a *whatever real number, including one and on the other hand zero.

In case -2 * 0, zero takes the whole identity of number -2: The number being negative and even; as a result we get ”just” zero. Similar happens in 2 * 0 = 0.

“Unique Sphere Shows Standing Out”

*Image courtesy of Stuart Miles at FreeDigitalPhotos.net*

My two cents: Zero ”zeroes” any number except itself. It ”zeroes” the whole identity – including a number being even or uneven – of any number except from itself; in case 0 * 0 = 0 zero keeps the identity of its own, it doesn’t ”zero” itself, which reflects the identity of zero itself, how it is neutral in a deep sense and meaning.

Mathematical philosophically zero refers to *none*, there isn’t something at all. Still, zero refers different than nothing. As I’ve written before emptyness (”zero”) can be created, *nothing *can’t be created; it is from which the creation begins.

Let us assume, that we have two (2) coins. It’s even amount of coins. Let’s give one coin to a poor beggar. Now we have only one coin, uneven amount of coins. We’ll give that coin to a poor beggar too. Now we have no coins at all, the number of coins we have is zero. Do we have still again even number of coins, as we have zero amount of coins? I mean, we don’t have coins left at all!

The coins we had were in a wallet and the two coins were all we had there; now the wallet is empty. Is emptyness even or uneven? Or are we speaking now about different matter?

As far as I can see, if the number of something is different than zero, there must exist something, somehow. This number is even or uneven.

So, number being even or uneven, philosophically would refer to existence; something must somehow exist, that is, the number of something is different than zero. This amount can be negative or positive, even or uneven, but not zero.

But if something doesn’t exist, the amount of this something is zero, that isn’t even or uneven, as stated before. If the “number of something” is even or uneven, something *must *exist, somehow.

Technically one test to determine, that is a number even, is to divide the number to be tested by 2; if reminder is zero, the number is even. This test is suspicious to zero from two (2) reasons:

- 0 /
*a*= 0 anyway were the number*a*whatever real number (except zero) - Two (2) is greater than zero by its absolute value (philosophical mathematical problem)

My two cents: Zero is neutral element in addition and one of its properties is, particularly philosophically, that as to being even or uneven, it is neutral.

(As a sidenote something came into my mind from section 2 above: Is number one (1) somehow fundamentally uneven in natural numbers set?)