11 there are multiple ways of writing out a given complex number, or a number in general And while $1$ to a large power is 1, a number very close to 1 to a large power can be anything. The complex numbers are a field
It's a fundamental formula not only in arithmetic but also in the whole of math The reason why $1^\infty$ is indeterminate, is because what it really means intuitively is an approximation of the type $ (\sim 1)^ {\rm large \, number}$ Is there a proof for it or is it just assumed?
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. 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 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.
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). 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.
