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Oct
21
answered Are there any open mathematical puzzles?
Oct
19
comment Are there any open mathematical puzzles?
Goldbach's conjecture?
Oct
15
comment Where did mathematicians learn how to do truth tables?
@CharlesStewart: Sure, WIttgenstein wasn't incapable of understanding higher mathematics and I'm sure he would have been able to create new higher mathematics had he pursued it. I just haven't seen any evidence though of his writing's (all philosophical) influences on mathematicians (um...yes...Kripke wrote about him but wrote philosophically about Wittgenstein's non-mathematical philosophy).
Oct
5
comment Improbable vs Impossible?
'almost impossible' is not 'exactly zero' in any natural or informal language; that goes against any useful definition of 'almost'.
Sep
16
awarded  Yearling
Aug
16
comment Connecting finite automata and regular languages in teaching/applications
Yes, these are all good examples of uses of finite automata either in design or analysis of engineering systems, but does their interpretation as regular languages add anything meaningful? Well, Kleene closure really needs to be used meaningfully.
Jul
22
awarded  Popular Question
Jun
22
comment Transformation of matrix
So are you only allowed matrix operations? You want a 'closed' form that you can then manipulate? If you just want the results of such a matrix, just notate it: $A^{*}_{i,j} = A_{i, i+j}$ or 0 if $i>j$.
Jun
19
comment Where did mathematicians learn how to do truth tables?
Yes, the specific strand of culture is difficult to specify, because there are language/nation separations (in addition to the faculty differentiation), but academic borrowing, too. Also, the 20th century has seen a lot of changes in communication, which complicates the matter. If forced, I'd have to limit it to English speaking culture (where things might be likely to have been borrowed from German or French, and doubtfully from Russian or Polish (but that would be very interesting!))
May
29
answered Can $\frac{n!}{(n-r)!r!}$ be simplified?
May
19
comment Why the terms “unit” and “irreducible”?
@user42912: 'unit' is not defined in your given definition. If you look at a definition, a unit divides a multiplicative identity, commutes with everything, and so has many similar properties to the multiplicative identity, which is often given the name '1' because it is so much like the integer 1.
May
8
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?
May
8
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.
May
6
awarded  Caucus
May
6
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).
Apr
13
awarded  Popular Question
Apr
6
comment Do factorials really grow faster than exponential functions?
nice and simple.
Apr
6
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).
Apr
5
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?
Apr
1
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?