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
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
Is it really impossible to use hexagons for mixed-resolution cover? The cases a and b are invalid by restrictions 1 and 2 The case c by restriction 3 PS: about “to split a DGGS cell”, for an exact definition, see DGGS standards or this animation About "Finite satisfatory limit" (restriction 4) see National and Global applications of DGGS, por example to solve the Land Ownership by approximating X⁻ zones
geometry - Find the angle ADB - Mathematics Stack Exchange Let x be the length of AE You can find the length of AD as the arccosine of angle DAE multiplied by x You can use the law of sines on triangle AEB to find the length of AB in terms of x, and then the law of sines on triangle ABD to find the desired angle (with the variable x conveniently cancelling out)