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| bio | website | |
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| visits | member for | 2 years, 8 months |
| seen | May 9 at 10:59 | |
| stats | profile views | 423 |
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May 8 |
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Is mathematics one big tautology? @IttayWeiss: It can be random/arbitrary. Usually that level of arbitrariness is only explored by logicians (something 'what if you don't have the axiom of pairing?'. I will agree with you that it is not the most popular or most productive research, and that directed exclusion is more fruitful ('What if you drop the axiom of infinity?'). But, really, were semigroups, loops, or quasigroups studied for themselves before groups had been axiomatized? |
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May 8 |
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Is mathematics one big tautology? @IttayWeiss: few sane mathematicians do so. some interesting math can be created by taking an axiom system and denying one or more axioms at a time and seeing what kind of system it produces. Its not always very productive, but it is one kind of exploratory method. |
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May 6 |
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Are all prime numbers finite? To add to the confusion, one can manipulate an object called 'infinity' in many ways similar to the manipulations that govern natural numbers. But one does not refer to infinity in common parlance as a number (presumably a natural number). |
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Apr 6 |
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Do factorials really grow faster than exponential functions? nice and simple. |
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Apr 6 |
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There are no bearded men in the world - What goes wrong in this proof? This is math? Its a question of vagueness of words...a philosophical problem (but then math is what good philosophy should try to be). |
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Apr 5 |
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Why don't we study algebraic objects with more than two operations? So I'm guessing that you don't count vector spaces (because the dot and scalar and vector and cross product are not on the same 'level'). So how about the reals which have an addition, multiplication, exponentiation (binary), all sorts of unary operations (elementary functions), etc. Or did you mean abstract algebras? |
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Apr 1 |
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Formula for the $1\cdot 2 + 2\cdot 3 + 3\cdot 4+\ldots + n\cdot (n+1)$ sum Clever...but how did you do the magic to think of converting $k(k+1)$ to the inner two terms of a cubed binomial? |
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Apr 1 |
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Formula for the $1\cdot 2 + 2\cdot 3 + 3\cdot 4+\ldots + n\cdot (n+1)$ sum You just did their homework! |
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Mar 30 |
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Why can't you flatten a sphere? @ilya: Psychology? Math is -all- about psychology. |
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Feb 19 |
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Understanding calculus formulas intuitively What's intuition for you? Is it a picture of a graph? Then try to draw some at first, then try to visualize later, and it'll become easier. The algebra is to notate precisely what the visions are, to keep the visions clean, and you manipulate the algebra because manipulating visual artifacts are not so precise. In a proof, the manipulations might correspond to something visual (and it is useful to make that correspondence when feasible), but sometimes the smallest algebraic step is just playing with the formalism that just isn't there in the visualization. |
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Feb 12 |
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Is 'no solution' the same as 'undefined'? Don't you mean the other way around? |
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Nov 30 |
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Where did mathematicians learn how to do truth tables? Interesting. 1) it is unclear who you are saying did what (who is 'they'?). Is it Russell/Frege? Truth Tables are not done in BR or GF sources, but they are in Wittgenstein, therefore my question. 2) Can you cite any references which support this? I'm curious about the train of provenance. |
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Oct 27 |
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Modifying Euler Totient Function So this takes as long as factoring N, right? (plus, the computation of the terms in the sum) |
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Aug 1 |
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Is there a Hamiltonian path for the graph of English counties? Nice! quick and easy. |
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Aug 1 |
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Is there a Hamiltonian path for the graph of English counties? Kudos...but magic trick over. Now you have to tell us how you did that. By hand or by running algorithm (if so then by what system)? And also, how did you create such a nice picture? You lifted it somewhere? There's no shame in that, but at least give a link. |
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Jul 28 |
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Trouble with filling out a Cayley table $u*u = p$. What is $u*u*u$? |
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Apr 25 |
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History of dot product and cosine The dot product as an explicit algebraic operation is not so necessary to the 'dischord of appearances', it is the $a d + b e + c f$ a decidedly open calculation in comparison to the obscurantist length of a vector and angle formula (requiring much more machinery). Any idea if this (what Hamilton knew) was popular before Gibbs? |
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Apr 10 |
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How do you explain the concept of logarithm to a five year old? @DanNeely: Yes, you're right. There are many contexts where an explanation could work/be meaningful and useful to a 5 yar old (JohnS keeps coming up with good ones). I think I was caught up in the symbol manipulation. But I still think the simple 'number of digits' concept, which would totally work for older kids (8-10 yoa) would be obscurantist to even a curious 5 year old. |
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Apr 8 |
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How do you explain the concept of logarithm to a five year old? To a -5- year old? Aren't you stretching the limits of relevance? Most (even bright) kids are only about to 'get' negative numbers (which is arguably a much prior concept (inverse of addition) that is much more accessible. If this is just for fun (for a child that can 'get' things), then @JohnS's example looks to be aan excellent idea with lo-tech/lo-conceptual overhead. |
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Mar 29 |
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Bounding ${n \choose k}$ ${n \choose k}$ increases up to $k = \lfloor n/2 \rfloor$, then goes down. So you only really need to worry about the left side up to the max. |
