Every even number is followed by an odd number.
Every odd number is followed by an even number.
If there are numbers that are both odd and even (we’ll call these odd-even numbers), every odd-even number will be followed by another odd-even number (because of the odd characteristic, making the next one even, and because of the even characteristic, making the next one odd).
Conversely, if there is an odd-even number, it is there because the previous number was odd-even.
So, is infinity odd or even?
Let’s take a physics perspective on this, and say that we haven’t observed the state of infinity (whether it’s odd or even), and that until we observe it, it’s both at the same time – that is, it’s odd-even.
By my fourth statement, if infinity is odd-even, the number one less than infinity is odd-even, and the number one less than that is odd-even, and the number one less than that… until you get to 1.
Therefore, all numbers are odd-even.
That is, all numbers are simultaneously divisible by 2 and not divisible by 2.
See the weird results of applying physics in maths, and not the other way round?