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
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
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
Who first defined truth as adæquatio rei et intellectus? António Manuel Martins claims (@44:41 of his lecture quot;Fonseca on Signs quot;) that the origin of what is now called the correspondence theory of truth, Veritas est adæquatio rei et intellectus
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
Is there a logical fallacy for confusing means with ends? In general, people don't confuse the means with the ends Instead, what happens is that people get so wrapped up in the means that they fail to see that the means aren't accomplishing the ends It's a reality-break, akin to the old saw about doing the same thing over and over, expecting different results Your anecdotal patient isn't forgetting that the end is sleep; the patient has convinced
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 question itself
linear algebra - Ridge Regression - Mathematics Stack Exchange Does anyone know how to justify or prove that the statement quot;ridge estimators of regression coefficients are always unbiased quot; is false? That was my first question, second, can you help me
Duty and Inclination in Kants ethics - Philosophy Stack Exchange Even after updating the original post there remain at least two different questions: How does morality relate to duty and inclination according to Kant? Kant’s Groundwork for the Metaphysic of Morals starts " Nothing in the world - or out of it - can possibly be conceived that could be called ‘good’ without qualification except a GOOD WILL " According to Kant an action has moral value