I am not sure if this is the idea of the exercise, but if you formulate "there are infinitely many primes" as for some property P, then it can also be stated as .
I was given this excersise as homework and to a certain extent i do understand what they are asking, but don't know where to start.
Consider "there are infinitely many primes". Find a suitable universe U of elements so that this theorem can be reformulated in the form : A (is a subset of) B
We were also told that we dont need to prove anything here.
Thank you for any suggestions.
A simple set up I came up with (which was similar to his answer) was:
Let U be the Set of all Sets (even though it's understood that there's no set of all sets), and let B be the set of all infinite sets. Moreover, let A be a subset of this set but also having the condition of being the set of primes.
Therefore A (is subset of) B (is subset of) U. ... sorry for not writting the symbol.
Does this sound right?