Why is $1 i$ equal to $-i$? - Mathematics Stack Exchange 11 There are multiple ways of writing out a given complex number, or a number in general Usually we reduce things to the "simplest" terms for display -- saying $0$ is a lot cleaner than saying $1-1$ for example The complex numbers are a field This means that every non-$0$ element has a multiplicative inverse, and that inverse is unique
factorial - Why does 0! = 1? - Mathematics Stack Exchange Intending on marking as accepted, because I'm no mathematician and this response makes sense to a commoner However, I'm still curious why there is 1 way to permute 0 things, instead of 0 ways
What is the value of $1^i$? - Mathematics Stack Exchange There are infinitely many possible values for $1^i$, corresponding to different branches of the complex logarithm The confusing point here is that the formula $1^x = 1$ is not part of the definition of complex exponentiation, although it is an immediate consequence of the definition of natural number exponentiation
abstract algebra - Prove that 1+1=2 - Mathematics Stack Exchange Possible Duplicate: How do I convince someone that $1+1=2$ may not necessarily be true? I once read that some mathematicians provided a very length proof of $1+1=2$ Can you think of some way to
Sum of 1 + 1 2 + 1 3 +. . . . + 1 n - Mathematics Stack Exchange 33 There is no simple closed form But a rough estimate is given by ∑ r=1n 1 r ≈ ∫n 1 dx x = logn ∑ r = 1 n 1 r ≈ ∫ 1 n d x x = log n So as a ball park estimate, you know that the sum is roughly logn log n For more precise estimate you can refer to Euler's Constant
Why is $1$ not a prime number? - Mathematics Stack Exchange 49 actually 1 was considered a prime number until the beginning of 20th century Unique factorization was a driving force beneath its changing of status, since it's formulation is quickier if 1 is not considered a prime; but I think that group theory was the other force