Reputation
Next tag badge:
990/1000 score
290/200 answers
Badges
26 283 572
Impact
~4.2m people reached

Oct
19
comment Stoll, Set Theory and Logic (pg 165): Logic for P->Q and P<->Q
He’s right because that is in fact how the conditional $\to$ is defined in propositional logic. You may feel that he hasn’t given you an adequate explanation of why we define it that way, but that’s a separate issue. (And I can assure you that Bob would not have taken kindly to being called a weasel!) In fact I agree that he could have done a better job of giving an intuitive justification of the third line, but his justification of the fourth line is quite reasonable.
Oct
19
revised Stoll, Set Theory and Logic (pg 165): Logic for P->Q and P<->Q
edited tags
Oct
19
answered Any example of open set of first category?
Oct
19
comment Find a closed expression for the sum of the entries of the Pascal triangle inside the upper n x n rhombus.
@jinha: Excellent! You’re welcome!
Oct
19
comment Cylindrical Shell Volumes Problem
@JXXII: You’re welcome! (And yes, $\pi/2$ is right.)
Oct
19
comment Cylindrical Shell Volumes Problem
@JXXII: When you revolve the strip at $x$ about the $y$-axis, the radius of the shell is $x$, not $1-x$. The integral that you set up calculates the volume obtained when you revolve the same region about the line $x=1$: the distance from an $x\in[0,1]$ to that axis is $1-x$.
Oct
19
comment Find a closed expression for the sum of the entries of the Pascal triangle inside the upper n x n rhombus.
@jinha: Does the addition to my answer make it clearer? I could just as well have run the inner sum from $m=k$ to $k+n-1$, but the extra terms are all $0$, and I usually think of Pascal’s triangle in the rectangular form.
Oct
19
revised Find a closed expression for the sum of the entries of the Pascal triangle inside the upper n x n rhombus.
added 467 characters in body
Oct
19
answered Find a closed expression for the sum of the entries of the Pascal triangle inside the upper n x n rhombus.
Oct
19
comment Cylindrical Shell Volumes Problem
@JXXII: I spend a lot of time here, so if you do ask another question, I’m quite likely to see it. If you want to make it almost certain, you can also leave a comment here addressed to me, with a link to the new question, and I’ll take a look the next time I’m on-line.
Oct
19
comment Cylindrical Shell Volumes Problem
@JXXII: You’re welcome!
Oct
19
comment Cylindrical Shell Volumes Problem
@JXXII: Yes, that looks good.
Oct
19
comment Cylindrical Shell Volumes Problem
@JXXII: Yes, $$V=2\pi\int_0^3\left(3x^2-x^3\right)\,dx\;,$$ but that integral isn’t $2\pi$. What did you get for the antiderivative?
Oct
19
answered Let $k \le \frac{n}{2}$, and suppose that $F$ is an antichain in $P(n)$ such that every $A \in F$ has $|A| \le k$. Prove that $|F| \le \binom{n}{k}$
Oct
19
answered Cylindrical Shell Volumes Problem
Oct
19
comment Are there any whacky orderings of R?
@Anthony: The OP did not impose any algebraic requirements on the order.
Oct
19
comment A property of discrete spaces
@Jonathan: Wikipedia tells me that some people do use the term Fréchet space to mean $T_1$ space, but in over $40$ years of doing topology I don’t recall having encountered the usage.
Oct
19
answered Are there any whacky orderings of R?
Oct
19
comment A property of discrete spaces
@Jonathan: A Fréchet space is one in which a set is closed if and only if it’s sequentially closed; this doesn’t really have much to do with separation properties.
Oct
18
comment A property of discrete spaces
@Jonathan: $X$ being Fréchet can’t be a necessary condition, since it’s not implied by $X$ being Hausdorff. In fact it turns out that Hausdorffness of $X$ is necessary and sufficient.