3
votes
1answer
53 views

writing papers: definition in word or formula?

If we write papers, is it or is it not desirable to write definitions in formulas AND words. So if I want to define the following set: $$S:=\{ x \in \mathbb{N} : P(x) \}$$ where $P$ is some predicate ...
0
votes
1answer
32 views

How could I define this $\mathrm{nw}(X)$ by using only one sentence?

A family $\mathcal N$ of subsets of a topological space $X$ is a network for $X$ if for every point $x\in X$ and any neighbourhood $U$ of $x$ there exists an $M \in \mathcal N$ such that $x\in M ...
3
votes
2answers
219 views

Can mathematical definitions of the form “P if Q” be interpreted as “P if and only if Q”? [duplicate]

Possible Duplicate: Alternative ways to say “if and only if”? So when I come across mathematical definitions like "A function is continuous if...."A space is compact ...