factorial

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

2024 Sep 13

linear algebra

Does anyone know how to justify or prove that the statement "ridge estimators of regression coefficients are always unbiased" is false? That was my first question,

2025 Jun 28

World Weather Map

Interactive world weather map by Worldweatheronline with temperature, precipitation, cloudiness, wind. Animated hourly and daily weather forecasts on map

2025 May 09

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

2025 Aug 10

What are the criteria for "bad faith" questions?

The main criteria is that it be asked in bad faith. ;-). I''m not entirely insincere: The question is rather how can we tell that, and a big part of the answer is "context"; it''s not mainly the

2026 Feb 16

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)?

2026 Feb 12

Who first defined truth as "adæquatio rei et intellectus"?

António Manuel Martins claims (@44:41 of his lecture "Fonseca on Signs") that the origin of what is now called the correspondence theory of truth, Veritas est

2025 Nov 19

trigonometry

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 $15.983$

2024 May 09