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"All the disputes that for so many generations have vexed philosophers are destroyed by visible certainty, and we are liberated from wordy arguments."


Dec
17
comment How many ways can seven people sit around a circular table?
@OllieFord: I usually blame that sort of thing on posting from my phone.
Dec
17
comment How many ways can seven people sit around a circular table?
@OllieFord: $7 - 1 = 6$.
Dec
16
answered How many ways can seven people sit around a circular table?
Dec
8
awarded  Caucus
Nov
28
revised What is the correct term (and symbolic representation) for specific “un-modded” values?
Repair title.
Nov
28
comment What is the correct term (and symbolic representation) for specific “un-modded” values?
Come to think of it, what is the property $x \equiv x+k\cdot(b_u-b_l),\,\forall k\in\mathbb{Z}$ even called? It's not quite mod, is it?
Nov
26
asked What is the correct term (and symbolic representation) for specific “un-modded” values?
Nov
16
accepted Incomplete statement of commutativity of summation in Concrete Mathematics?
Nov
16
comment Incomplete statement of commutativity of summation in Concrete Mathematics?
Got it: I was thinking only of reorderings.
Nov
16
comment Incomplete statement of commutativity of summation in Concrete Mathematics?
Ah , I wasn't seeing that I could conclude that $\sum\nolimits_{p(k)\in K}{a_{p(k)}} = \sum\nolimits_{k\in K}{a_{p(k)}}$ (presumably since $\sum\nolimits_{p(k)\in K}{a_{p(k)}} = \sum\nolimits_{p(k)\in p[K]}{a_{p(k)}} = \sum\nolimits_{k\in K}{a_{p(k)}}$) — I mean I saw it, but wasn't seeing that it followed from what had been said so far in the text. Is that right? Also, I'm not clear about why $p$ needs to be a permutation of anything beyond $K$.
Nov
16
comment Incomplete statement of commutativity of summation in Concrete Mathematics?
Nice (and very helpful) answer! I see how this is probably a better (more general) way to think about it. But isn't it about something a bit different. Specifically, $q:\Bbb Z\to\Bbb Z:k\mapsto k+3$ is not a permutation of $K$ (though it is a renaming). Would it be right to say then that my reformulation is correct (and needed for the manipulations in the text) if $p$ and $q$ are limited to being permutations; but that the original formulation is sufficient if $p$ is a renaming?
Nov
15
comment Incomplete statement of commutativity of summation in Concrete Mathematics?
@ZachGershkoff: It might; I don't know (I always think of sets as unordered unless told otherwise, but I'm not an expert); that may be part of the answer and would address the first part of the issue. The bigger part of the question would remain though.
Nov
15
asked Incomplete statement of commutativity of summation in Concrete Mathematics?
Nov
6
asked Can I reconstruct Penney's game win probabilities from dominant strategy odds?
Oct
23
comment Dividing by 2 numbers at once, what is the answer?
+1 for "convention voodoo" to describe the fabrications "educators" think they need to come up with to avoid teaching real concepts (like multiplicative inverse).
Sep
28
comment What is required to establish the law of cosines?
Just to be sure: is there a subtlety to "the standard inner product on $\mathbb{R}^n$" that I should watch for? Could you elaborate on what an inner product that might not qualify would look like?
Sep
28
accepted What is required to establish the law of cosines?
Sep
28
comment What is required to establish the law of cosines?
So if the inner product space is in $\mathbb{R}^n$, then it just turns out that $\left<a|b\right>/\|a\|\|b\|$ (which is defined for an inner product space) equals $\cos \theta_{a,b}$, where $\theta_{a,b}$ is based on a concept of angle in $\mathbb{R}^n$ (which is defined elsewhere). We then call any $\theta_{a,b}$ that satisfies this relation in any inner products space an "angle". Correct?
Sep
4
awarded  Popular Question
Jul
2
awarded  Curious