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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?
Apr
1
comment Formula for the $1\cdot 2 + 2\cdot 3 + 3\cdot 4+\ldots + n\cdot (n+1)$ sum
You just did their homework!
Mar
30
comment Why can't you flatten a sphere?
@ilya: Psychology? Math is -all- about psychology.
Mar
23
awarded  Popular Question
Feb
19
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.
Feb
12
comment Is 'no solution' the same as 'undefined'?
Don't you mean the other way around?
Jan
20
awarded  Nice Question
Jan
9
awarded  Good Question
Nov
30
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.