so I am an architecture student trying to get into the programming game so I'm taking a concepts of math corse at Carnegie Mellon. I'm horrible at writing proofs. I have no idea where to start even. but I get the concepts part. so I need to write a proof for why The Cartesian product of set R x N is uncountable. I think I know that it's because R is uncountable so that alone means that there is an uncountable amount elements in the set containing the solution. but how do I write the proof formally? am I even correct so far!? please help!
I learned all about countable sets being plugged in to a function that outputs some N and is bijective. so I know how to do the proof if it were just R. I also know about cardinality and how for something to be bijective it must have the same cardinality.