# Is 0 is an even and positive number?

#### WWW

A friend of mine told me that (by his teacher) 0 is an even and positive number, how can it be?

#### arildno

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0 is definitely an even number, since it may be written as 2*n, where n is some integer.
I think it's more usual to say that 0 is a non-negative number, but I'm not sure..

Staff Emeritus
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0 is definitely not a positive number. Positive means greater than zero, and zero is certainly not greater than itself.

#### The_Imagizer

for as far as I know, 0 is both positive and negative.

I suppose I will hear no argument if I say that 0 is in both N+ and N-, so that pretty much solves it, no?

#### master_coda

All the definitions of positive numbers that I've ever seen exclude zero. So zero is not a positive number. However it is true that it is an even number.

#### NateTG

Homework Helper
Both or Neither

Depending on the situation, zero may be considered to be positive, negative, both, or neither.
In some computers, negative and positive zero may be different, but in normal mathematics, whether zero is considered to be positive depends somewhat on context.

#### WWW

By standard logic there is the excluded middle rule.

Is there any influence based on this rule and the definition of 0 (positive, negative, both, or neither)?

#### matt grime

Homework Helper
It is a matter of convention. To avoid confusion one should say things like strictly positve and so on. It is no different from saying greater rthan and not specifiying if we mean strictly or posisibly equal. It shuold be no great hardship to make oneself clear.

#### WWW

Is there any formal and rigorous way to show the difference between 'strictly positive' and 'positive'?

What is 'posisibly equal'?

Last edited:

#### matt grime

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"What is 'posisibly equal'?"

A typo. It should read possibly.

#### HallsofIvy

Homework Helper
NateTG said:
Depending on the situation, zero may be considered to be positive, negative, both, or neither.
In some computers, negative and positive zero may be different, but in normal mathematics, whether zero is considered to be positive depends somewhat on context.

I wouldn't consider computer practice to say anything at all about mathematics!

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