Recent content by mathwonk

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 y = 0 corresponds to x =1, this is equivalent to saying that the derivative of its inverse function at x=1 is equal to 1. But the inverse function has...

short calc is a first course in calc, less than 300 pages, terse, no epsilonics. Undergrad analysis is a 3rd course in calc, very rigorous, over 600 pages. if you look\ on amazon you can read the impressive table of contents for the undergrad analysis.

@PeroK: I like your suggestion to use previously proved general theorems to deduce discontinuity of specific functions. One such theorem I like is the intermediate value theorem, that the continuous image of an interval is also an interval. This shows immediately that the function f which...

I apologize for provoking sad faces by post #12. To be honest, most people will not need to give an actual proof of sequential convergence to be convinced it holds, so epsilons, N's, and deltas can be kept in the background. E.g. in the example of midgetdwarf, we can pretty much assume that...

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.

In fact, when stated precisely, the sequential version is even more complicated, i.e. it is being abbreviated above by the unexplained phrase “{xn}—>a”. The full definition of that symbol of course is: “for all epsilon, there is N such that, for all j, j≥N implies |xj-a|< epsilon”. Hence the...

A little symbolic logic notation is useful for easily negating basically anything. I.e. to negate, you exchange the type (universal vs existential) of the quantifiers and then negate the statement. I.e. the negation of "for all ( ), for some [ ], for all < >, P", is just "for some ( ), for all...

watching the movie Ivanhoe today I was interested in the height of the famous fall off the castle by the great stuntman Paddy Ryan, reputed to be 100 feet into a moat. So I timed it at about 2.5 seconds. Given Newton's law (which goes back to Galileo) the distance fallen in 2.5 seconds should...

I think your new book is probably a good choice.

yes they meant what you said. however this is a strange definition, as property 3 follows from property 2, so is not needed. The book seems to be confusing two different characterizations. Namely given a topology on X, one wants to define a base for that topology, which is properties 1 and 2...

the fact that the natural numbers contain an infinite number of disjoint infinite subsets, implies for the arithmetic of infinite cardinals, that if A is the cardinal number measuring the size of the natural numbers, then A.A = A. On the other hand if 2^A denotes the cardinal number of all...

or, forgive me, maybe gently discuss it with her; after all, its another chance to spread the word, and that is what teaching is of course.

A family member in Tennessee, had a neighbor, an author, who once inscribed one of his books for her. Many years later, recognizing his name, I pulled that book off the shelf in a large used book store in Salt Lake City, and saw his inscription to her in the inside cover. Another time, while...

you seem to be asking for very extreme comparisons, but in the general direction of whether a significantly smaller boxer can win, I suggest you watch a film of the Jack Dempsey/Jess Willard fight; but only if you have a strong stomach for seeing the punishment absorbed by Willard, who...