@Bibas. Well all this thing has come while i solved the problem of probability. My point is you can't put zero in an even or odd number.r Thats why i didn't consider probability of zero in the question.


@3X  There are several complication while considering multiplication and division (in your case 0 divided by 2) of zero as per defining any set or rule in mathematics.  Hence division and multiplication of zero cannot be used to define evenness or oddness.

Let me give you one example,

Take an equation,

0=0    ( zero equals 0)

This equation can be re written as,

1²-1²=(1-1)<sup>2           (both side is again 0=0  as you may agree )

or, (1-1) (1+1) = (1-1) (1-1)


Now, taking out common term (1-1) from both side result,


1+1=1-1

2=0      Really?

You know this is not true. 

Let me tell you how this result came. The result came because of treating zero as any positve real natural number.  we treated term (1-1) divided by (1-1)     equals to 1.   Algebraically it may be true because x divided by x =1.
See how zero has made mockery of algebric equation that we have been doing all our life.

However, in reality  this term is zero divided by zero  and we we should not be  treating it as equal to 1.

Remember how we avoided zero in derivatives by taking limit tends to zero and not equal to zero.

My point is zero cannot be bound by any mathematical relation and define it in any set. We should leave zero as it is . It is neither negative nor positive, neither prime or neither non prime, neither odd nor even, anything divide by zero results infinity which is unmeasurable, any number multiplied by zero is zero .

So we know zero doesn't give one answer rather a set of answers for everything. So to say it is just divisible by 2 shouldn't make it count as even because zero gives similar result for everything. And even accepting the division, multiplication of zero for defining mathematical relations have resulted in many complication.

Some striking question about zero is,

How would you divide 0 which doesn't exist evenly among people ?

We know opposite of  1 is -1,  2 is -2. But what is opposite or negative number of 0.  Its like saying what is opposite of RED?

The fact is zero lies in borderline of everything.  negative and real positive number, set of odd and even numbers.

Lets put an analogy,
Remember days of physics when we read   how magnetic north and south pole points to nowhere in a borderline where earth north and south pole have similar effect. At that point we dont know whether we are closer to north pole or south pole because strength of both are same.

Same can be said about zero being in  a borderline of all the set of numbers.

I for one have never considered zero as an even.</sup>