During a rather creative stint last night, I came up with the following idea which considering basic logical operators and the addition of even and odd numbers.

Anyone familiar with basic logic knows what the XNOR operator is and what it does, but for the sake of thoroughness, here's a basic run through: In a simple logic table, the XNOR operator returns a True iff (if and only if) both the inputs are True or False. If one inputs a True and a False, the answer is False. Essentially, the XNOR operator only produces a True if the input is homogeneous.

The nature of even and odd numbers has an identical relationship to the XNOR operator concerning addition. For example, let's set some thing as equivalent. First, let's assume that if a number is even, it's the same as putting a value of True into an XNOR expression. Then, let's say that if a number is odd, it's the same as putting a value of False into an XNOR expression. Before we go on, let's look at a basic property of addition of even and odd numbers.

When one adds two odd numbers, one gets an even number (3+7=10).
When one adds two even numbers, one gets an even number (6+12=18).
When one adds an even and an odd number, one gets an odd number (13+8=21)

It should become quite obvious to the reader that even and odd numbers, when also considered as equivalent to True and False, exhibit the exact same behavior as an XNOR operation. Funky, no?

Note: The kind user Brontosaurus brought to my attention that the same properties are true when multiplying nonzero numbers with different signs (IE a + times a + is +, a - times a - is +, and + times - is -).

Note: Although I can't think of why this would change anything, this whole node refers to real integers. As far as I can figure out, decimals, irrationals, and imaginary numbers don't really make sense in terms of odd and even numbers.