Reputation
4,700
Top tag
Next privilege 5,000 Rep.
Approve tag wiki edits
Badges
16 37
Impact
~206k people reached

Mar
4
comment Recurrence representation(s): $a(n+1)=a(n)(n-1/2)+o(1/n)$ and $a(n+1)=a(n)(n-1/2+o(1/n))$
I'm not sure I understand the connection with the Kendall-Mann numbers. The K-M numbers at oeis.org/A000140 have a combinatorial interpretation but no closed form function or even a recurrence. The numbers defined at oeis.org/A181609, despite the title, just seem to be equal to K-M for the first few then start to diverge. How is A181609 associated with K-M?
Mar
4
answered How can I prove the formula for calculating successive entries in a given row of Pascal's triangle?
Mar
3
comment Why did mathematicians take Russell's paradox seriously?
My point was that the paradox -is not- a contradiction in the system. The fact that you can evaluate '$P \land \neg P$ ' to get '$F$' does not mean there is a contradiction in propositional logic, just that a contradiction implies falsehood there. I feel like (in hindsight obviously) that Russell's paradox is not a problem with the system (it still may be consistent), but a problem with the (natural) human idea that 'set' can applied to any collection.
Mar
3
comment Why did mathematicians take Russell's paradox seriously?
But I take issue with the metaphor, in that it connotes that foundations are -totally- useless. Practically, it's easy to see that bridges are staying up (mostly) without them (the Babylonians did OK with mostly unproven facts, not needing the foundations of Euclid's axiom system). But one characteristic of modern mathematics is discovering the foundations under the foundations, at every level. My math history is rusty, but didn't $\epsilon-delta$ pave the way for modern (20th C) analysis?
Mar
3
comment Why did mathematicians take Russell's paradox seriously?
Excellent...thanks for expositing...that was my main concern, that I was having 20-20 hindsight, unaware of the conditions of thought at the time.
Mar
3
comment Why did mathematicians take Russell's paradox seriously?
@Paul VanKoughnett: "By Russell's paradox proper, there's also no set of groups...". Really? At least for those straightforward algebras, I thought those collections were sets (or small categories).
Mar
2
asked Inequality on balls/bins with nested logs
Mar
2
comment Why did mathematicians take Russell's paradox seriously?
@Arturo Magidin: Despite what's already been said, I agree with the intent of the title question...shouldn't people have responded immediately 'Yes, of course that's a contradiction, so that means the described set (the set of all sets) just doesn't exist' (and so no need to worry further) ? There's no contradiction in -math-, just a contradiction in that particular statement. Yes, so comprehension can't be applied successfully arbitrarily, but that doesn't mean 'math' falls apart.
Mar
2
comment Is this identity involving Stirling numbers of the first kind well-known?
It's not trivial, but the constant, 3, is just big enough not to be important enough to be even an exercise in a text. But it's perfect for OEIS as noted below.
Mar
1
answered Is the 'variable' in 'let $y=f(x)$' free, bound, or neither?
Mar
1
comment Matrix multiplication: interpreting and understanding the process
I feel like this is then a question about history: why did (= what historical motivations) matrix multiplication get defined like it is? Did the dot product (which is itself magical in that it gives a projection) come first?
Feb
28
answered Indicate reverse of graph transition
Feb
28
comment Element-Wise Proofs?
The crucial step, from 2nd to 3rd statement, is not obvious (at this level). How do you justify the manipulation of English 'and's and 'or's?
Feb
28
revised How to detect antitransitivity from an adjacency matrix?
added new explanation
Feb
28
comment How to detect antitransitivity from an adjacency matrix?
I'm going to be a bit intrusive and say that you really shouldn't want a 'measure' of how transitive a graph is. A graph is either transitive or it is not (all it takes is one edge to prevent it). There might be a fractional version of this 0-1 property (sort of like fractional chromaticity) but I'm not fluent enough with that to come up with a meaningful fractional-transitive property. Instead I think you want to get rid of cycles (in a directed graph). Then you can take a transitive closure to get the 'is-a' poset. I'm editing my answer to reflect this.
Feb
27
comment Factorial and exponential dual identities
Excellent...it took me a while to appreciate. Sometimes even the simplest manipulation can be inscrutable, like the integral equal to $\frac{1}{1-t}$. What this all does for me though is convince me in the simplest way possible that the second identity is just the best analytic continuation of the factorial function (just the simplest way that is).
Feb
27
accepted Factorial and exponential dual identities
Feb
27
comment Factorial and exponential dual identities
Excellent! Thanks. How did you come to know that? As usual the algebra is almost trivial after the fact. Any hints as to the meaning import (like Qioachu's question in his 2nd link)?
Feb
23
comment The ratio in terms of sets
Can you clarify your question? Your first question asks about A/B, which is then $\frac{(2n-1)!!}{4^n}$, and you second asks about A which you seem to have answered already.
Feb
23
answered How to detect antitransitivity from an adjacency matrix?