Dec 22, 2021
I encounter this riddle in the chapter exercises of Infinite Large Napkin of Evan Chen in Algebra chapter.
It says “My Love for you has a subset isomorphic to itself”.
Non intuitive thinking, it is Absurd because how can a subset can be a subset isomorphic to itself unless it is contain or the set itself.
Now, consider the set of integers Z and even integers 2Z.
Z := {…,0,1,2,…}
And 2Z := {0, -2,2,-4,4,….}
It is clear that 2Z is properly contained to Z but at the same time isomorphic to Z because we can find a bijection from Z to 2Z, nonetheless, the riddle implies that if a subset is isomorphic to itself then this set mus be infinite.
Talking to the context above, we say
My Love for you is infinite.