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There are multiple measures of what that comes to but intuitively you might think that the value alternates between 1 and 0, so you could call it a half But truly, i would always say $2=1+1$ simply because the symbol $2$ should reasonably be defined as that. In truth this series never converges on any given number

Depending on how you define addition, the sum to infinity is not properly defined In the end, it's all just a matter of definitions You might argue that the sum of those numbers is 1 if $\infty$ is an odd number and $0$ if $\infty.

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? 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

11 there are multiple ways of writing out a given complex number, or a number in general The complex numbers are a field Since $\ {1\}$ has only two subsets, $1=\ {1\}$ Option 1 is possible, since identifying $1$ with the empty set is perfectly valid, but it's much more natural to identify $0$ with the empty set.

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First, a concrete example of things that can happen with complex exponentiation if you aren't careful: $1 = e^ {2\pi i}$, so we can naively try to compute $1^i = (e^ {2\pi i})^i = e^ { (2\pi i)i} = e^ {-2\pi}$. The formal moral of that example is that the value of $1^i$ depends on the branch of the complex logarithm that you use to compute the power. You may already know that $1=e^ {0+2ki\pi. How do i calculate this sum in terms of 'n' I know this is a harmonic progression, but i can't find how to calculate the summation of it Also, is it an expansion of any mathematical function

In fact, quite often, one limits himself to structures where $1+\cdots+1\ne 0$ no matter how many times you add $1$ to itself

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