I The number zero

1. Apr 16, 2016

Dacu

Good morning,
How do we prove that the number zero is a negative or positive number?

2. Apr 16, 2016

Staff: Mentor

Zero by definition is neither positive nor negative so there is no proof for it.

Here's a brief discussion on Zero:

from wikipedia:

https://en.wikipedia.org/wiki/0_(number)

3. Apr 16, 2016

Dacu

Why zero , in France , can be a negative or positive number?
My reasoning:
1) $$0>0$$ involves $$0=0+a$$ where $$a>0$$ and involves $$0+a>0+a$$ and $$a>a$$ and this is false.
2) $$0<0$$ involves $$0=0-a$$ where $$a>0$$ and involves $$0-a<0-a$$ and $$-a<-a$$ and this is false.
So the number zero can not be negative or positive.What was supposed to prove.My proof is correct?

4. Apr 17, 2016

Staff: Mentor

I doubt that this is correct. By definition of the terms negative and positive, zero is neither negative nor positive.
You have started with a false assumption; i.e., that 0 is larger than itself. No finite number can be larger than itself, nor can it be smaller than itself.
You're starting with a false assumption here, as well.

From wikipedia, https://simple.wikipedia.org/wiki/Positive_number
A positive number is a number that is bigger than zero.

The definition for negative number is similar.

5. Apr 17, 2016

jbriggs444

By another definition, zero is both negative and positive. I was taught to use the terms "strictly positive" and "strictly negative" in order to avoid the resulting potential for ambiguity. On the other hand, that class was some forty years ago and fashions may have changed.

6. Apr 19, 2016

Ssnow

This fact

or this

doesn't convince me ...

7. Apr 19, 2016

Samy_A

(bolding mine)
Probably the confusion is just a matter of definition.