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seen Aug 12 at 15:56

A mediocre professor at a top-notch university making mediocre contributions to this top-notch community


Mar
25
comment Explain to me what these symbols mean.
The confusion often arises from the fact that many writers call $dy/dx$ a "symbol" as if it were atomic, but then later start doing algebra with it. This leads to the question, "well, then what is $dy$ really?"
Mar
10
comment Summation of element of a subset and divition
I think your two added assumptions are reasonable enough to make the original question interesting. But 8 feels quite arbitrary now.
Mar
8
comment Summation of element of a subset and divition
Technically, it is true: the empty set is always a subset of $A$ and 8 divides 0.
Mar
6
revised How to prove $\det(e^A) = e^{\operatorname{tr}(A)}$?
edited title
Mar
1
comment Continued Fraction [1,1,1,…]
You're welcome. This is the cutest (and most elementary) solution I could think of. Good luck.
Feb
26
answered Continued Fraction [1,1,1,…]
Feb
26
comment Continued Fraction [1,1,1,…]
I think this is the argument the OP already has but is worried about. But thanks for the lovely typesetting nonetheless. :)
Feb
16
awarded  Yearling
Feb
14
answered Prove that if $n$ is a composite and $p \gt \sqrt[3]n$, then $n/p$ is a prime.
Jan
19
comment Given $N$, find $ab = N$ with $a$ and $b$ as close as possible
Correct, which is why I was careful to not claim that it was. If you know an efficient (meaning poly-time) factoring algorithm, please send me a private note and we'll write a paper. Or start a company. Or be captured/assassinated before we can do either...
Jan
19
comment Given $N$, find $ab = N$ with $a$ and $b$ as close as possible
Factoring is thought to be hard. Knapsack is NP-Hard, and therefore thought to be hard. If $P = NP$ then all of these are poly-time solvable, but that's unlikely. The best known general factoring algorithms are super-polynomial (on a conventional computer; quantum algorithms are polynomial-time).
Jan
19
answered Given $N$, find $ab = N$ with $a$ and $b$ as close as possible
Dec
30
accepted Derivation of $e$
Dec
30
revised Derivation of $e$
added 75 characters in body
Dec
30
comment Derivation of $e$
@JonasMeyer: I think the way math evolved was to use some informal versions of infinite series without any rigorous notions of limits (see for example the Madhava series, used around 1400CE, en.wikipedia.org/wiki/Madhava_series). In any case, in my question I meant "how can we derive a method to calculate digits of $e$ from the definition of Bernoulli, but without resorting to the Taylor series".
Dec
29
asked Derivation of $e$
Dec
28
revised question about derivative of exponential function
deleted 4 characters in body
Dec
19
awarded  Good Answer
Dec
10
comment Easy way to generate random numbers?
Check out en.wikipedia.org/wiki/… (that's what you're trying to devise here).
Dec
9
comment Planar graphs & Spanning trees
To even have red, blue, and green spanning trees, every node must have at least degree 3, but you can't have more than $3|V|-6$ edges.