I see, that's interesting! I've never seen it solved like this, on both sides of the expression...
0<|x-4|<E/4+1
-E/4-1<|x-4|<E/4+1
But that does lead to a contradiction in this problem, and works if you plug in the limit as 16.
Well that is wonderful...but it is still strange that we...
Right, so if you try and prove a limit that is not true, where exactly in the proof is there a contradiction? There isn't. There should be. That is my point.
The square root example I'll try and make analogous to this problem, but I don't think it really works. You prove that you square any...
I am a first year freshman at UC Berkeley, in Math 1A. We learned the delta-epsilon proof for proving the limit of functions. I won't go through a whole proof or anything, but the general idea is you have a delta that is less than |x-a| (and greater than zero) and an epsilon less than |f(x)-L|...
I also want to know the answer to this. I think you're asking what are the mechanics of the atom, so that it "wants" to have 8 electrons in its outer shell. Can someone please give a good answer to this? I want to know and I feel like (no offense) no one who answered understood the question.