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OK, Neon\u00c2\u00a0. Figured it out.. Axis 2017
Q:<\/p>\n
How to prove that the subset of $ \\mathbb{Z} $ generated by $\\mathbb{Z} \\cup \\{2\\}$ is neither $ \\mathbb{Z} $ nor $\\mathbb{Q}$?<\/p>\n
If I take the subset of $\\mathbb{Z}$, i.e. the finite set of integers which contains the elements $0$ and $1$, and choose $2$ as an element. This means that $2$ has an inverse but all elements of this subset have an inverse. Hence the question becomes this: How to prove that the subset of $\\mathbb{Z}$ generated by $\\mathbb{Z} \\cup \\{2\\}$ is neither $ \\mathbb{Z} $ nor $ \\mathbb{Q} $?<\/p>\n
A:<\/p>\n
We have $\\mathbb{Q}\\subseteq \\{2\\}$ and $\\mathbb{Z}\\subseteq \\{0,1\\}$, and the only such unions are $\\mathbb{Z}\\cup\\{2\\}$ and $\\mathbb{Z}\\cup\\{0,1\\}$.<\/p>\n
A:<\/p>\n
Hint: Consider the set $\\{x\\in\\Bbb Z\\;:\\;x
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