Ok so I'm tutoring for a class this term which is supposed to be an intro to mathematical proofs. One kid asked me how to understand sentences like "Let x and y be real numbers then x = y or x =/= y.". I'm over simplifying, between - it's the use of anonymous variables that seems to bug them. I told them to read it as "for any real number values x and y take, the following holds". Not sure if it was the proper way to explain it, but they came back at me with the more complicated question of universal generalization, e.g. proving something for an arbitrary x and concluding it holds true for all such x. I'm having a really hard time explaining those things. Although they are implicitly clear to me, I can't really make them clear for others. Can anyone give me an explanation for those two things that beginners would understand? Also, can someone give me tip about explaining this kind of stuff?