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
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
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
What is mathematical basis for the percent symbol (%)? It's a convention that started sort of as a fluke In a 14th century Italian manuscript, a sideways letter P is written to stand for 'per 100' or 'per cento' It then slowly evolved A more in depth bit can be found under the percent sign history here, and on the wiki page In addition to percent 0 0, and permil 0 00, there is also permyriad 0 000 for 1 10000
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
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