Is undefined really undefined?

Question

In math, when you graph a line where x=1 or 2 or 3 etc the line is straight up and down. So for example when its y=, your line is left to right (walk left to right) but when its x= than it would be (walk down to up), but cant x= be used in other ways, or is just undefined?

2nd question. Can 0 equal something other than itself? examples: 2 times 0=0 14 divided by 0=0. I can understand that in mathematical terms 0 is just 0. But in science is it the same or can 0 actually equal something else. I've recently learned that black holes have mass, but they dont weigh anything, could it be possible that when matter enters its event horizon and enters it the black hole then becomes heavier?

Answer 1

1) "We" say that x=Constant has a slope that is undefined.  That is "we" are saying that division by zero does not produce a real number.

2) Don't confuse the "fact" that several things equal zero with zero equaling many things.  Zero is a construct of number theory and it took a long time to be "discovered" in the history of math...see Boyer 2nd edition of "A History of Mathematics".

Hope this gets you started.

-Fred