# Thread: Zero as number like all the others

1. ## Zero as number like all the others

I dont know if this is the right place to place this question. The other day i started thinking a lot about this, and it just won't get out of my mind. Why does zero has the properties of any other number? Maybe the question should be, "why shouldn't it?"
1+1+1 = 3x1

n x n = n^2

n( n+1)= n^2 + n

why can N be replaced by 0 and all properties still hold?

why does 3*0 = 0, and 0*0*0=0^3 and still its the same as 0?

why does zero has properties like N x 0 =0 for any N

i can't even explain my question in good terms, its just a brainwashing of non-intuition on my mind, which i cannot get rid of, and its destroying my intuitions. Can someone help me believing again that 0 is a number like any other??

2. ## Re: Zero as number like all the others

I really don't understand your question. 0 is a number like all others and, like all other numbers, it is "unique"- it has some properties that other numbers do not. Yes, 0 times any number is 0, just as 2 times any number is even.

Abstractly, that property comes from the fact that 0 is the "additive identity" (x+ 0= x for any number) and the distributive law (a(b+ c)= ab+ bc).

x(y+ 0)= xy+ x0, by the distributive law.
x(y+ 0)= xy since 0 is the additive identity. Since xy+x0= x(y+ 0)= xy, we have xy+ x0= xy and, subtracting xy from both sides, x0= 0.

3. ## Re: Zero as number like all the others

Originally Posted by DarkFalz
I dont know if this is the right place to place this question. The other day i started thinking a lot about this, and it just won't get out of my mind. Why does zero has the properties of any other number? Maybe the question should be, "why shouldn't it?"
1+1+1 = 3x1

n x n = n^2

n( n+1)= n^2 + n

why can N be replaced by 0 and all properties still hold?

why does 3*0 = 0, and 0*0*0=0^3 and still its the same as 0?

why does zero has properties like N x 0 =0 for any N

i can't even explain my question in good terms, its just a brainwashing of non-intuition on my mind, which i cannot get rid of, and its destroying my intuitions. Can someone help me believing again that 0 is a number like any other??

If on three consecutive days I give you zero apples, how many apples do you have?

(I assume you haven't eaten or given away any)

CB

4. ## Re: Zero as number like all the others

The thing is that i made the mistake of thinking too much about things. But zero also behaves the way it should in nature. F=m*a which means that for each mass unit we have 1 unit of "a" acceleration to equal the force. With 0 mass we have 0 force cuz we have 0*a acceleration units. Its just that it fits so well in everything. But what messes me the most, is things like this 0( 0+1) = 0*0 + 0*1 and still it all reduces to 0. Zero absorbs an complex formula, such that 0( A COMPLEX FORMULA) =0
its such a powerful concept

5. ## Re: Zero as number like all the others

The thing is, 0 also behaves as expected with nature, F=m*a works even for m=0 or a=0. Is it that 0 is so much connected to nature that it perfectly resembles it?