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- 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
- 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
- Formal proof for $ (-1) \times (-1) = 1$ - Mathematics Stack Exchange
Is there a formal proof for $(-1) \\times (-1) = 1$? It's a fundamental formula not only in arithmetic but also in the whole of math Is there a proof for it or is it just assumed?
- 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
- 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
- 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
- If $A A^{-1} = I$, does that automatically imply $A^{-1} A = I$?
This is same as AA -1 It means that we first apply the A -1 transformation which will take as to some plane having different basis vectors If we think what is the inverse of A -1 ? We are basically asking that what transformation is required to get back to the Identity transformation whose basis vectors are i ^ (1,0) and j ^ (0,1)
- General term formula of series 1 1 + 1 2 + 1 3 . . . +1 n
This sum is called $H_n$ the $n$th"harmonic number" and has no known closed form
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