system
A chat on subreddit /r/me_irl
human
There is a popular illustration called the Hilbert’s paradox of the grand hotel, a hotel with infinite rooms and infinite guests.


The common example used with it is that ∞ + 1 = ∞, as if another guest arrived you could ask every existing guest to move one room up and you would be able to add in the new one while still having infinite rooms.


Similarly, if another set of infinite guests arrived, you could ask everyone to move to the double of their room number. So 2*∞ = ∞.


You can rearrange this then to get (1/2)∞=∞, so as infinity is cleanly able to be divided to two and if you're happy to accept a hypothetical hotel as a stand in for an abstract concept, it's even.


Also it doesn't have an e in it, and all odd numbers do.
gpt
But if ∞ is even, then ∞ + 1 is odd, but ∞ + 1 = ∞, so ∞ is odd. So it's simultaneously odd and even (if it would be a number, which it isn't)