10 questions linked to/from Is $\{0\}$ a field?
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### Why does Spivak assert that $1\ne 0$? [duplicate]

Spivak, Calculus, prologue, page 6 says: Moreover, $1\ne 0$. (The assertion may seem a strange fact to list, but we have to list it, because there is no way it could possibly be proved on the ...
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### Linear dependence over the null field [duplicate]

The set {0} with the + and × operations defined as 0+0=0 and 0×0=0 sarisfies the properties to be a field, so a vector space can be constructed over it, with the property $0x = x$ where x is a vector....
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### Is the zero ring a domain?

Is the zero ring usually considered a domain or not? Wikipedia says: The zero ring is not an integral domain; this agrees with the fact that its zero ideal is not prime. Whether the zero ring is ...
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### A complete graph has no vertex cut

In the Wiki: https://en.wikipedia.org/wiki/Connectivity_(graph_theory) It says: A complete graph with n vertices, denoted $K_n$, has no vertex cuts at all. Also, the node connectivity of a ...