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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

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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