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Why is $1 i$ equal to $-i$? - Mathematics Stack Exchange 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 While $1 i = i^ {-1}$ is true (pretty much by definition
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
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
If $A A^{-1} = I$, does that automatically imply $A^{-1} A = I$? A -1 A means that first we apply A transformation then we apply A -1 transformation When we apply A transformation we reach some plane having some different basis vectors but after apply A -1 we again reach to the plane have basis i ^ (0,1) and j ^ (1,0)
power series - How can we know the answer to 1-1+1-1+1 . . . The series does not converge, because as you observe, the partial sums $1,0,1,0,\ldots$ oscillate and do not approach a single limit There are various ways to assign values to some divergent series, such as Cesaro summation, regularization, etc See here for some information specific to this series
What does $QAQ^ {-1}$ actually mean? - Mathematics Stack Exchange I'm self-learning Linear Algebra and have been trying to take a geometric approach to understand what matrices mean visually I've noticed this matrix product pop up repeatedly and can't seem to de