Sorry, this is probably a really stupid question. But I'd appreciate an answer
What is the difference between DELTA Y and EPSILON when solving limit proofs?
Sorry, this is probably a really stupid question. But I'd appreciate an answer
What is the difference between DELTA Y and EPSILON when solving limit proofs?
So, the definition of is that .
Whew, that's a mouthfull, so let's break that down some. Firstly, the condition is say that for any positive number , (no matter how super-small!), I can come up with another number so that when my x is a -distance away from c, will be within -distance from L.
Think of the condition like a game. Someone gives you a number . All you know about it is that it's positive. You get no other information. What you're trying to do is pick a (you pick ) so that the condition of the limit is satisfied.
Just to clarify, let me work out an easy example. Say you want to compute . Let be given (I don't know what it is, but it's a fixed number). Now, I need to pick a so that my limit is satisfied. But, in this case, , so let . That is, for whatever number you give me, I'll pick my to be the same thing!
So, let's test that this works. Suppose that . Then, quite necessarily, precisely because I'm assuming that . I hope that clears up how this process works.