Mitch
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 May8 comment 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? May8 comment 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. May6 awarded Caucus May6 comment 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). Apr13 awarded Popular Question Apr6 comment Do factorials really grow faster than exponential functions? nice and simple. Apr6 comment 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). Apr5 comment 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? Apr1 comment 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? Apr1 comment Formula for the $1\cdot 2 + 2\cdot 3 + 3\cdot 4+\ldots + n\cdot (n+1)$ sum You just did their homework! Mar30 comment Why can't you flatten a sphere? @ilya: Psychology? Math is -all- about psychology. Mar23 awarded Popular Question Feb19 comment 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. Feb12 comment Is 'no solution' the same as 'undefined'? Don't you mean the other way around? Jan20 awarded Nice Question Jan9 awarded Good Question Nov30 comment 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. Oct27 answered solve $n^{{1/2}^k} = 1$ for $k$ Oct27 comment Modifying Euler Totient Function So this takes as long as factoring N, right? (plus, the computation of the terms in the sum) Sep16 awarded Yearling