Does any one know is zero is odd or even?

Answer 1

Zero is neither even nor odd. The thing that makes zero special from other numbers is how it represents the absence of numerical value.

Answer 2

Surely the (relatively) modern invention of zero is a symbol used to show that 'there is nothing here' - it's a dilemma, of course, to represent the absence of things with a physical symbol! a concept much more easily accepted in algebraic terms by a letter. Maybe zero is at best a compromise - an accepted symbol (a thing obviously 'existing' in imagination) which we employ so we work mathematically. Let 0 = oranges then 1 - 0 = 1, you have taken no oranges away from 1. Let 0 = the planets in the solar system then 1 - 0 =1, you have taken no planets away from 1. Zero represents the absolute absence of all things but it exists in itself! How can the absence of all things be odd or even? However when we use zero as part of the symbol to represent a group of, say, 10 things the zero part takes on the property of making an even number and 10 - 2 is an even number. Maybe the definition of an even number should be a multiple of 2, not wholly divisible by two. I don't know basically, it's a bugger as we say in Sheffield.

Answer 3

Zero became a part of the Natural Numbers System.
If one defines evenness or oddness on the integers (either positive or all), then zero seems to be taken to be even; and if one only defines evenness and oddness on the natural numbers, then zero seems to be neither. This dilemma is caused by the fact that the concepts of even and oddness predated zero and the negative integers. The problem posed by this question is that zero is not to be really a number not that it is even or odd. ITS NEITHER

Answer 4

Forget dividing by 2 and turn the argument upside down.

If you divide an even number by another even number you get a result that is either an integer or a fraction but has a concrete value. If you divide 2 by zero the result is infinity which is not a concrete number.

Therefore zero cannot be even.

The same arithmetic applies to odd numbers; but if you divide 3 by zero the result is infinity, which is not a concrete number.

Therefore zero cannot be odd.

The mistake is to think that because something lies between two odd integers it must be even, whereas clearly, something with no value can be neither odd nor even.

Maths or logic it's got you coming AND going.

Answer 5

What a load of poorly defined arguments. Integers are whole numbers either positive or negative. Are you people arguing that zero is a whole number and is it positive or negative. Shall we move on to the square root of minus one. It seems like the only place to go with these imaginary theories.
The answer is yes but they are in a small minority. Is zero odd or even NEITHER

Answer 6

Very clever question Ray L. An even number is one that can be divided by two (into two even parts with nothing left over!). Zero indicates that there is absolutely nothing there to be divided. Therefore zero cannot be divided into two equal parts nor into two unequal parts. The interesting thing though is that when zero is represented on a scale such as an X - Y plot, it occupies a point that is in the sequence of even numbers rather than in the sequence of odd numbers. Zero would be even except that it has no value and cannot be divided. Therefore zero is neither even nor odd; and that is really odd.

Answer 7

Zero is even. An even number is one that leaves no remainder when divided by two. Zero divided by two is zero, with no remainder, so zero is even.

Michael P's answer, something about how zero is not a number, is, well, completely wrong. Sorry. :-)

For more info, see the article below. Hope that helps!

Answer 8

Zero is not a number but a lack of a number and therefore can be neither odd nor even. There is also absolutely no need to define what you ask in your question. However, and more interestingly, any number divided by infinity always, by definition, equals zero, and that number can be odd or even to start. However, infinity is impossible to define as a proper number so that view breaks down ..... zero is unique in that it has no numerical property ... it is merely a mathematical line or base ..... don't forget you can go below zero and have negative or minus numbers ......... which may qualify to be odd or even .... but you need to pass zero to do that .... looking at it that way, zero is merely a marker and not a number as such to qualify in some way.

Answer 9

Look what you've started!!
I have always been told that zero is neither odd nor even.
I do, however, understand people's argument about its divisibilty by 2 but no number is no number. Sorry.

PS Maybe this is another one for Stephen Hawking!

Answer 10

Good question. Let's apply this ruleset:

odd + odd = even
even + even = even
odd + even = odd

Same number plus itself = even. 0 + 0 = 0. Therefore, 0 must be even.

Likewise using the same ruleset, odd + 0 = odd which also suggests 0 is even.


----- FOLLOW UP AFTER READING OTHER ANSWERS -----
Odd or even is a property. The property is commonly assigned to values. Zero is not a value, yet we can still apply the descriptive property to the zero state.

Answer 11

Zero is an odd question, and even if you could depend on the answer.