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Canada-0-BALCONIES Azienda Directories
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Azienda News:
- factorial - Why does 0! = 1? - Mathematics Stack Exchange
The theorem that $\binom {n} {k} = \frac {n!} {k! (n-k)!}$ already assumes $0!$ is defined to be $1$ Otherwise this would be restricted to $0 <k < n$ A reason that we do define $0!$ to be $1$ is so that we can cover those edge cases with the same formula, instead of having to treat them separately We treat binomial coefficients like $\binom {5} {6}$ separately already; the theorem assumes
- Possible references for semigroup approach to Markov processes
Although I'm not anything remotely close to an expert (quite the opposite really), it seems to me that the standard reference for the kind of things you're looking for is the book Markov Processes: Characterization and Convergence by Ethier and Kurtz, which studies Markov processes through the lens of operator semigroups in a systematic (and very general) way For a "friendlier" and more
- What does it mean to have a determinant equal to zero?
Your answer is already solved, but I would like to add a trick If the rank of an nxn matrix is smaller than n, the determinant will be zero
- Prove by induction that $n! gt;2^n$ - Mathematics Stack Exchange
Hint: prove inductively that a product is $> 1$ if each factor is $>1$ Apply that to the product $$\frac {n!} {2^n}\: =\: \frac {4!} {2^4} \frac {5}2 \frac {6}2 \frac {7}2\: \cdots\:\frac {n}2$$ This is a prototypical example of a proof employing multiplicative telescopy Notice how much simpler the proof becomes after transforming into a form where the induction is obvious, namely: $\:$ a
- What is the difference between Fourier series and Fourier . . .
What's the difference between Fourier transformations and Fourier Series? Are they the same, where a transformation is just used when its applied (i e not used in pure mathematics)?
- Recover a real, not a np. float64 notation - Mathematics Stack Exchange
How can I get simply the real value 608 3296641637677 as result, and not that the whole script np float64 (608 3296641637677) ?
- When 0 is multiplied with infinity, what is the result?
What I would say is that you can multiply any non-zero number by infinity and get either infinity or negative infinity as long as it isn't used in any mathematical proof Because multiplying by infinity is the equivalent of dividing by 0 When you allow things like that in proofs you end up with nonsense like 1 = 0 Multiplying 0 by infinity is the equivalent of 0 0 which is undefined
- Finding common ancestors in DAG - Mathematics Stack Exchange
I'd like to implement some new algorithm for discovering common ancestors in genealogical software I found an article with a relevant name Finding Common Ancestors and Disjoint Paths in DAGs but
- trigonometry - Why are angles in degrees converted into degrees . . .
As an example, I downloaded some GPS data from my camera the other day in which I found numbers like $4215 983 $ This turned out to represent $42$ degrees and $15 983$ minutes If you go to a particular latitude and longitude on Google Maps it will show the latitude and longitude both in degrees with a decimal fraction and also in degrees, minutes, and seconds with a decimal fraction
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