Short, quick problem with Integers

  int Number = Number + 1; // adds one to int number, I think?

Whenever you have doubts, consult documentation. Forums are a place for secondary problems - things that the documentation doesn't cover. For an intro course, you should not be afraid to ask a professor or teaching assistant such a question.

I think that your problem is that you declare Number inside the loop Function - thus it is initialized every time loop runs and is not using the previous value.

In other words, you said, "int Number" twice. That creates two variables called Number. Google "C++ scope".