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Extended real numbers as algebraic structure
I need to work with real numbers, but extended to have an additional element. This element, I denote by $\odot$ and my set is: $\mathbb{R}_{\odot}=\mathbb{R}\cup\{\odot\}$. This element should behave ...
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Is the element $(0,0,0)\in\mathbb{R}^3$ a divisor of zero?
(I'm assuming that $\mathbb{R}^3=\mathbb{R}\times\mathbb{R}\times\mathbb{R}$)
In my assignment, I'm told to prove that exactly one of the following can be true for an element $(x,y,z)\in\mathbb{R}^3$
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