Recent content by magnoliamkt

r was a rational number (as per the original question statement). I think I do understand this now though - sorry for the confusing post (I'm new to using this forum and the math language). Thanks for your help! :)

Let me make sure I'm following you: Choosing a sequence r_n of rational numbers k/n close to an irrational number x \Rightarrow \left|x-r_n \right|< \epsilon (epsilon) maybe? And then... lim \ r_n = x. So we have that because lim of both f(r) and g(r) equal to an irrational number x (or q in...

I could see how it might be useful, but no we haven't proved it yet, so I don't know if I could validly use it.

Homework Statement Let f, g be continuous from R to R (the reals), and suppose that f(r) = g(r) for all rational numbers r. Is it true that f(x) = g(x) for all x \in R?Homework Equations The Attempt at a Solution Basically, this seems trivial, but is probably tricky after all. I know that...