mathwonk's latest activity

are z1, z2 complex variables? if so, the zeroes of an analytic function of 2 complex variables are never isolated.

It helps to have a definition of e. One definition is that e is the unique base such that the derivative of e^y at y=0 equals 1. Since...

short calc is a first course in calc, less than 300 pages, terse, no epsilonics. Undergrad analysis is a 3rd course in calc, very...

You already solved the differential equation here so it might be hard to tell what it was. The differential equation originates from...

f is clearly not continuous at 0 (sequential def makes it obvious with any sequence xₙ→0) but it's continuous everywhere else since...

@PeroK: I like your suggestion to use previously proved general theorems to deduce discontinuity of specific functions. One such...

I apologize for provoking sad faces by post #12. To be honest, most people will not need to give an actual proof of sequential...

midget dwarf, nice example, but there is a typo in your statement; likely you meant f(0) = 1, but f(x) = 0 for x ≠ 0.

Rule of thumb: If you want to prove that something is continuous, use Epsilon delta definition of limit. If you want to disprove...

In fact, when stated precisely, the sequential version is even more complicated, i.e. it is being abbreviated above by the unexplained...

A little symbolic logic notation is useful for easily negating basically anything. I.e. to negate, you exchange the type (universal vs...

No but hyperreals could offer a check on your answer which I realize is a poor second to, getting the epsilon-delta proof correct in an...

An alternative, which is equivalent to the usual epsilon-delta definition is: A function ##f## is continuous at a point ##a## if for...

watching the movie Ivanhoe today I was interested in the height of the famous fall off the castle by the great stuntman Paddy Ryan...

I think your new book is probably a good choice.