RBarryYoung
Reputation
Next privilege 125 Rep.
Vote down
 2d comment Why did mathematicians introduce the concept of uniform continuity? To be clear, "practical application" and "application to a theorem" are completely different things. Jan11 comment Why are primes considered to be the “building blocks” of the integers? For instance, you could formulate a "unique sum theorem" if you limited the "additive primes" to just the number one(1). This is not really very interesting nor useful as it merely restates what Peano's fifth(?) postulate already clearly implies. And there's no interesting structure or re-combination to a system consisting of a single prime only. Jan11 comment Why are primes considered to be the “building blocks” of the integers? @MattGregory No, that's just it. There is no "unique sum theorem" known that is both interesting and useful, except those that are really just the Prime Factorization Theory(PFT) clumsily restated to avoid using multiplication. And since those are really PFT, they end up with the same "primes" as we have now. Same thing applies to powers. Dec4 comment Is there a shape with infinite area but finite perimeter? Sure. An infinitely long cylinder has an infinite area, but a perimeter length of zero. Of course, that's not in $\mathbb{R}^2$, which was not stated as a requirement, but may have been intended..? Sep25 comment Is it true to say that “it's not logically possible to prove something can't be done”? This is just a slightly smartened up version of the inane truism "You can't prove a Negative." Obviously not true in mathematics and formal system, but less obviously, not true in any common reasoning system that has a notion of "proof". What's really meant is "You can't prove a Universal.", at least not empirically. Scott Adams is brilliant, but he's definitely wrong on this one. Saying that you can't prove that anything can't be done is effectively equivalent to saying that you can't disprove anything. Jul28 revised Interview puzzle with a deck of cards, some cards upside-down correcting opposite of upside down. (keep missing pieces) Jul28 suggested approved edit on Interview puzzle with a deck of cards, some cards upside-down Jul20 comment Elementary theorems with several proofs? This probably should be a community wiki, since it does not have a single correct answer. Apr14 comment Limit is found using polar coordinates but it is not supposed to exist. OMG, I will upvote you just for the images if you'll tell us what you used to make them... Mar30 comment Why would you expand a square wave in a Fourier series? All modern digital audio uses the Fourier Transforms extensively, so knowing a square wave's Fourier series can be very helpful to understanding why, say, a hi or lo-pass filter changes its shape in various ways. learnabout-electronics.org/ac_theory/filters84.php Mar21 comment Why is $\sin^2x + \cos^2x = 1$ important? $\sin^2x + \cos^2x = 1$ is basically just the Pythagorean identity ($a^2 + b^2 = c^2$) expressed in Trigonometric terms instead of Algebraic terms. And that's important because the Pythagorean theorem is the basis for almost all trigonometry. Mar18 revised If the infinite cardinals aleph-null, aleph-two, etc. continue indefinitely, is there any meaning in the idea of aleph-aleph-null? Included theactual question into the body of the post. Mar18 comment If the infinite cardinals aleph-null, aleph-two, etc. continue indefinitely, is there any meaning in the idea of aleph-aleph-null? FYI: make sure that your actual question is in the body of your post. It's confusing to have it only in the title. Mar18 suggested approved edit on If the infinite cardinals aleph-null, aleph-two, etc. continue indefinitely, is there any meaning in the idea of aleph-aleph-null? Mar8 comment What is exponentiation? Exponentiation in the complex plane is a chiral operator. You cannot possibly have an intuitive or natural understanding of it without first grasping that. And the rest naturally follows from that. Feb14 comment Very probable event occuring at least once during $n$ trials Assuming that they are independent events (and/or that subsequent probabilities for the events are unaffected by prior ones). This was never actually stated in the question. Feb5 comment Why are there so few Euclidean geometry problems that remain unsolved? After some research I am no longer confident that my earlier statement about being resolvable in O(n) is correct. I had forgotten a few things (such as recursive enumeration, and that linear optimization problems can be restated as a problem of planar inequality bounding maximums), and now believe that I may have misunderstood the potential complexity of the transformation procedure. Feb4 comment Why are there so few Euclidean geometry problems that remain unsolved? @WillieWong Yeah, but its been 35 years since I worked on any of this. I am having a lot of trouble finding the references, or even recalling the proper mathematical terms to search for. :-( I'll try though. Feb4 comment Why are there so few Euclidean geometry problems that remain unsolved? @vonbrand Yes, unlike formalized Euclidian Geometry modern "interesting" branches of geometry, such as Projective Geometry, etc. extend (and/or modify) the Euclidian concepts a great deal and are not deductively complete and thus still fall into the realm of exponential proof searches. Feb4 comment Why are there so few Euclidean geometry problems that remain unsolved? @JasonDeVito No, by Godel's theorem and subsequent work any deductively complete formal system like EG (Euclidian Geomtery) has a lexical truth function that given any syntactically valid statement in the formal system, transforms it into an arithmetical expression that always returns 0/1 based on the truth of the statement. Both the transform and the expression are closed and so run in O(n) steps where 'n' is the length of the statement. I believe that EG's function was demonstrated back in the early 60's. As such, EG will never again have an unsolved problem, and is thus "uninteresting".