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  • complex analysis - Show that the function $f (z) = \log (z-i)$ is . . .
    Ok but the result ends up being the same, $u_ {xx} + u_ {yy}$ is never becoming zero since it is $\frac {x+y-1} {\sqrt {x^2 + (y-1)^2}}$
  • 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
  • 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
  • Integral of $\sqrt {1-x^2}$ using integration by parts
    A different approach, building up from first principles, without using cos or sin to get the identity, $$\arcsin (x) = \int\frac1 {\sqrt {1-x^2}}dx$$ where the integrals is from 0 to z With the integration by parts given in previous answers, this gives the result The distance around a unit circle traveled from the y axis for a distance on the x axis = $\arcsin (x)$ $$\arcsin (x) = \int\frac
  • 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
  • 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
  • metaphysics - How does philosophy define the concept of error and . . .
    This is not an answer to my question I did not ask what a judgment is First, how do you determine that a given fallacy is actually a fallacy? And second, how do you account for the fact that appealing to authority can be correct in certain contexts?Is an objective deviation from truth is an error? I don't think so
  • 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


















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