435 reputation
413
bio website in.another.dimension
location Athens, Greece
age 46
visits member for 3 years, 10 months
seen yesterday

Interests: math, programming and games, not necessarily in that order.

Favourite numbers: Surreals


Aug
20
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.
Aug
16
awarded  Yearling
Aug
16
answered Prove $2^{135}+3^{133}<4^{108}$
Jun
11
comment how to know of the number of real roots?
Which is what the OP asked: "polynomial to have exactly three distinct real solutions"
Jun
11
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.
May
6
awarded  Caucus
Apr
14
answered To find the logarithm of $1728$ to the base $2 \sqrt{3}$
Mar
12
comment Weird math question in ACT prep
What might be misleading? That you say "fraction" while you probably mean "proper fraction"?
Mar
11
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.
Feb
25
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.
Feb
25
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.
Feb
12
awarded  Civic Duty
Jan
12
awarded  Citizen Patrol
Nov
29
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).
Nov
29
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.
Nov
2
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.
Nov
2
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.
Sep
24
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.
Aug
24
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.
Aug
5
revised Evaluate $\lim\limits_{n\to \infty}\frac{1}{n+1}+\frac{1}{n+2}+\cdots+\frac{1}{6n}$
edited body