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  • 0 posts edited
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  • 195 votes cast
Mar
1
comment Tough contest problem
As sin(ix) = i sinh(x) (for real x) it is purely imaginary. So sin(sin(ix)) = i sinh(sinh(x)). Similarly for any more iterations of sin() and sin(sin(sin(sin(ix) = i sinh(sinh(sinh(sinh(x)))) is purely imaginary too. However cos(ix) = cosh(x) is purely real and taking cos() of this value three more times cos(cos(cos(cos(ix)))) is also purely real. Hence there is no solution to this equation on the imaginary axis. The imaginary solution(s) must lie somewhere else.
Feb
28
comment Tough contest problem
Alternative just looking at the imaginary axis putting ix for x and using cosh(x) = cos(ix) and i sinh(x) = sin(ix). I will play around with this a bit.
Feb
28
comment Tough contest problem
Cool use of Picard's Theorem! Makes sense to me. I was thinking of converting the sin() and cos() to expressions in exp()s but it gets pretty complex due to the nesting.
Feb
27
comment Tough contest problem
I know the question was for real x. I am curious if we allow complex x if there are solutions.
Jan
21
answered Why would a calculator have base 5?
Nov
20
answered Two people are looking for each other. Is it faster for both to actively search, or for one to search while the other stays still?
Nov
16
revised Intuition for a real line vs. a “hyperreal line”
added 78 characters in body
Nov
16
answered Intuition for a real line vs. a “hyperreal line”
Jul
23
answered Do groups, rings and fields have practical applications in CS? If so, what are some?
May
31
awarded  Yearling
May
23
comment Fractional Derivative Implications/Meaning?
You are right it can have a geometric interpretation just as the single integral can be interpreted as the area under the curve. And it is not a local geometric property as the tangent is. I am having trouble reading the small print in your question and if you are asking can you have arbitrary real numbers in the power of the derivative operator then I believe the answer is yes. Actually I have read you can even put complex numbers in there!
Feb
27
comment Fractional Derivative Implications/Meaning?
I added to my answer to say why it is non-local
Feb
27
revised Fractional Derivative Implications/Meaning?
added non-local reason
Feb
26
answered Necessary or sufficient conditions for rationality of a limit of a sequence of rational numbers
Feb
26
answered Fractional Derivative Implications/Meaning?
Feb
13
comment To what extent is the taylor polynomial the best polynomial approximation?
@5PM Thanks - that makes sense. I had misread the formula as f(k) with k = 0 to n. Works for f = p giving zero norm.
Feb
12
comment To what extent is the taylor polynomial the best polynomial approximation?
I may be misunderstanding something here but if I set f = p in your metric the first term is zero but the second term is not zero. But isn't the norm of 0 supposed to be zero?
Feb
6
answered How much Math do you REALLY do in your job?
Dec
5
comment Difference of differentiation under integral sign between Lebesgue and Riemann
In your right hand side is it supposed to be df/dx(x,t)dt evaluated at x = x0 and not df/dx(x0,t)?
Nov
22
answered Show that $\mathbb{Q}$ is dense in the real numbers. (Using Supremum)