Is there any number set that is used in that kind of equations without solution on the complex numbers?
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3Extended reals $\infty=\infty+1$. :) – IrbidMath Aug 02 '20 at 14:31
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How are the extended reals representated? – Perch Aug 02 '20 at 15:17
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Extended real numbers. We add two numbers to the real numbers namely $-\infty,\infty$ with $c\infty=\infty$ if $c>0$ and $-\infty$ if $c<0$. $\infty+\infty=\infty$ , $\infty-\infty$ undefined. Check
https://en.m.wikipedia.org/wiki/Extended_real_number_line
Clearly if you work with in $G$ for some set and you want to check the solution of and you each element have an inverse w.r.t $+$ then
$\begin{array}{ccc}x&=&x+1 \\ x-x&=&-x+x+1\\ 0&=&1\end{array}$
hence in our $G$ , we have $1=0$ i.e. $1$ is the addition inverse. But am sure you are not looking for something like this right?
IrbidMath
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