ypercube
Reputation
463
Next privilege 500 Rep.
Access review queues
 Aug20 comment math fallacy problem: $-1= (-1)^3 = (-1)^{6/2} = \sqrt{(-1)^6}= 1$? And I guess you mean that the main issue is not the (1)^3 = (-1)^(6/2) equality but the next one with the root. But some readers may be confused that you mean the second equality and not the third. Aug20 comment math fallacy problem: $-1= (-1)^3 = (-1)^{6/2} = \sqrt{(-1)^6}= 1$? I would add that it holds when b and c are integers but not necessarily when one (or both of them) aren't. Aug16 awarded Yearling Aug16 answered Prove $2^{135}+3^{133}<4^{108}$ Jun11 comment how to know of the number of real roots? Which is what the OP asked: "polynomial to have exactly three distinct real solutions" Jun11 comment how to know of the number of real roots? If with "3 distinct roots" you mean the roots to be 3 distinct numbers a, b, c and one of them a double root, then it's possible. May6 awarded Caucus Apr14 answered To find the logarithm of $1728$ to the base $2 \sqrt{3}$ Mar12 comment Weird math question in ACT prep What might be misleading? That you say "fraction" while you probably mean "proper fraction"? Mar11 comment Weird math question in ACT prep Why do you think that a and b are necessarily fractions? "Fraction" does not mean an (absolute) value of less than 1. Feb25 comment Prove that $1 + \dfrac{1}{2} + \dfrac{1}{3} + \cdots + \dfrac{1}{n} = \mathcal{O}(\log(n))$. I agree that it may be confusing but it's used in many Computer Science books. Feb25 comment Prove that $1 + \dfrac{1}{2} + \dfrac{1}{3} + \cdots + \dfrac{1}{n} = \mathcal{O}(\log(n))$. @Code-Guru The = in notation f(n) = O(g(n)), does not stand for equality. Feb12 awarded Civic Duty Jan12 awarded Citizen Patrol Nov29 comment Can every proof by contradiction also be shown without contradiction? @amWhy: You say "One of the advantageous to constructing direct proofs of propositions, when this is feasible, is that one can discover other useful propositions in the process. " I agree but proofs by contradiction (or rather, attempts to proofs) can also lead to wonderful discoveries (non-euclidean geometry comes to mind). Nov29 comment Can every proof by contradiction also be shown without contradiction? +1 Great explanation. Can you emphasize the affirmative answer?: So there are statements that are provable by contradiction that are not provable directly. Nov2 comment Spatial Geometry - Hole in Sphere And this question has the calculus solution: Given a solid sphere of radius R, remove a cylinder whose central axis goes through the center of the sphere. Nov2 comment Spatial Geometry - Hole in Sphere @rschwieb: No, that's a "well"-known puzzle. The volume does not depend on the radius of the sphere. Sep24 comment How is $e^x$ read aloud? I would vote that this question is off-topic for this site. Perhaps it would fit better at the English.SE one. Aug24 comment Theorems with an extraordinary exception or a small number of sporadic exceptions @AsafKaragila: Of course your theorem is a fallacy. It fails for number 10.