The power set of every infinite set is uncountable. An infinite set (as an element of the power set) cannot be defined by writing the infinite sequence of its elements but only by a finite formula. By ...
It happens a lot of times that when one defines a new object (ring, module, space, group, algebra, morphism, whatever) out of given data one first chooses some additional structure. And sometimes ...
Hi everyone, Disclaimer 1: logic and set theory are a long way from my field, so apologies in advance if I demonstrate extreme ignorance or stupidity, and please correct me if (when?) I write stupid ...
This is slightly related to question The unprecedented success of the “intersection” operator . Apart from a set of maths books of null measure, most have the following property: Objects ...
Consider the following statement of the Arzela-Ascoli theorem. Theorem. Let K be a compact topological space and let S be a subset of C(K). Then S is relatively compact if and only if S is uniformly ...
Is there a name for sets for which it is easier to test membership than to find members---and vice versa?
This is a question my son Bob asked me. For some sets it is relatively easy to test for membership but a lot more difficult to find members, and for others the reverse is true. Here is an elementary ...