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?

- Jul 29th 2010, 02:08 PMjakobsandbergWhat is the difference between DELTA Y and EPSILON when solving 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? - Jul 29th 2010, 09:12 PMMath Major
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. - Jul 29th 2010, 09:20 PMMath Major
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. - Jul 30th 2010, 03:13 AMHallsofIvy
Can you give an example of a problem "solving limits" that involves a "delta y"? I have seen many proofs that a limit is as claimed that involved "epsilon" and "delta" but I have never seen one that involved "delta y".