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location Cleveland Heights, OH
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Professor emeritus at Cleveland State University. I’m a set-theoretic and general topologist with an interest in combinatorics. I’m also interested in linguistics, especially historical linguistics.


Jun
19
answered What does the notation min max mean?
Jun
19
comment prove $A \sim B\implies 2^A \sim 2^B$.
@Hades200621: That’s okay; the most important thing is that it did help!
Jun
19
comment Help with a Function
@Jake: Interesting: I can’t think of any special significance that attaches to such points, or any good reason to give them a name. However, if that’s what’s wanted, you need only solve the equations $f(x)=1$ and $f(x)=-1$; these are both quadratics, so you’ll need nothing more than the quadratic formula.
Jun
19
comment Help with a Function
@Jake: Note that it’s not a parabola. I’m not sure what you mean by ‘y(1)’ and ‘y(-1)’; are you talking about the $y$-intercept, the place where the curve crosses the $y$-axis?
Jun
19
answered I'm gonna give probability regularization classes
Jun
19
revised Help with a Function
added 519 characters in body
Jun
19
comment Help with a Function
@amWhy: I don’t think that I’ve run into that terminology, but I’ll add a bit to cover the possibility.
Jun
19
answered prove $A \sim B\implies 2^A \sim 2^B$.
Jun
19
answered Help with a Function
Jun
19
revised Help with a Function
LaTeX, formatting.
Jun
19
comment Is this language regular?
It’s clear from his comment that @Johannes correctly understood the nature of $L$. Can you construct a DFA that recognizes $\{a^n\}^*$? That’s very straightforward, and if you have that, modifying it to recognize $\{\langle a^1,a^n\rangle\}^*$ is trivial.
Jun
19
answered Partial Order induced topology
Jun
19
answered What topics to include on a first course in number theory
Jun
18
answered Does every point in a $T_{3}$-space have a clopen base set or infinite nested base sets, none of which are clopen?
Jun
18
answered How to teach mathematical induction?
Jun
18
comment I know the basic definition of the continuity. But here, the definition is applied for "ball
@B11b: You’re welcome; I’m glad it helped.
Jun
18
answered I know the basic definition of the continuity. But here, the definition is applied for "ball
Jun
18
comment Is this proof complete? Case of a metric space
@dfeuer: Yes, $4$ was a typo for $3$.
Jun
18
answered Cardinal arithmetic questions
Jun
18
answered Closed subsets of $\mathbb{R}$ characterization