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location Sydney, Australia
age 48
visits member for 1 year, 8 months
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Jun
13
comment Is this question too easy or am I getting it wrong?
If I remember correctly (in Spivak's) $e^x$ is defined through its Taylor series and proved continuous that way.
Jun
12
comment Is this question too easy or am I getting it wrong?
Attention readers: this is the answer! The one flagged by the PO is a circular definition.
Jun
2
comment Identification of a curious function
@Yuval, I saw something similar when reviewing election strategies (as in Politics) in an election where people vote for a list of candidates, there is a number of places to be elected $N$ (say a senate), and lists get as many places as percentage votes won: $places = floor(N P_l)$. The tricky part was that there is a remanent after allocating all lists, as one cannot allocate a fraction of a place, an allocation then was from greatest residual to lowest. So, what's the best strategy, split the party in many lists or nominate a single one? Plotting, we arrive at something similar.
May
29
comment Logic and mathematical variables as objects
Also, the concept of valuation is from model theory. But it seems you want to "internalise" valuation for the variable type. So, sorry about the confusion; although you will need some sort of semantic for your logic anyway...
May
28
comment Logic and mathematical variables as objects
@Angelorf, I updated my pseudo-answer; good luck!
Apr
23
comment Digits of $n$ factorial
@Arthur, you are right is the most likely thing to happen. I bet looking at the Ring $Z_b$ where $b$ is the base, or even $Z_{b^L}$, being $L$ a fixed maximum length under consideration should settle the matter quickly. This also would explain, if this is the case, why the first digit (or any fixed length initial sequence) does not seem to be random.
Jan
12
comment Rational roots of polynomials
@StevenStadnicki, I preferred to multiply by X and add a free term. But still no luck... as said, interesting challenge.
Jan
12
comment Rational roots of polynomials
Is the problem any easier if indexes are swapped? It seems to me letting $a_n$ being the free term is an equivalent formulation. Interesting challenge, I wish I could add some more points to the bounty...
Jan
2
comment Semigroup implies exponential
Did it, hope ok. Tnx.
Jan
1
comment Semigroup implies exponential
@Byron.Schmuland, I am still confused by your use of I as opposed to I (identity) as used by the OP, could you please rephrase your answer, I still don't get it all :( ?
Dec
23
comment Semigroup implies exponential
Well, it should be in a text book. I have seen similar "semigroups" in image analysis (or multi dimensional signal processing) all the time. Not exactly like this, but certainly close. Tnx!
Dec
23
comment Semigroup implies exponential
Humble but important result, +1 from me. Is this part of some standard text book? I would like to know...
Dec
18
comment how many elements of S
@ronno, hum, you are right. The whole question is wrong anyway. I believe there is a typo from the OP.
Dec
18
comment how many elements of S
If entries are arbitrary, the question itself is wrong (or was mistyped). See my updated answer.
Dec
18
comment how many elements of S
@PraphullaKoushik, you were right, kind of. See updated answer :)
Jul
8
comment how to generate parametrically a matrix of positive determinant
I have added relevant context.
Jun
14
comment Supposedly simple integral
I just ran it through Mathematica (which has quite advance formulas and algorithms for integration)... and nothing. In all likelihood, there is no closed form.
Feb
15
comment Wavelet Transforms
I agree this is more a dsp.stackexchange.com question. By the way, as fas as I know, the discrete wavelet transform assumes uniform sampling. But sampling issues are general regardless of the transform. Why are you interested in wavelets?
Feb
14
comment Calderon's admissibility condition for wavelets explained
Thanks for the two pointers! I will have a deeper look.