Notations

\(\Bbb N      \qquad   \{0,1,2,3,\dotsc\}\)
\(\Bbb N^+\qquad   \{1,2,3,\dotsc\}\)
\(\Bbb Q^+\qquad   \{x|x\in\Bbb Q, x>0\}\)
\(\Bbb Q_+\qquad   \{x|x\in\Bbb Q, x\geqslant0\}\)
\(\Bbb R^+\qquad   \{x|x\in\Bbb R, x>0\}\)
\(\Bbb R_+\qquad   \{x|x\in\Bbb R, x\geqslant0\}\)

Number theory

\(p^\alpha\parallel a\qquad   p^\alpha\mid a, \text{but} p^{\alpha+1}\nmid a, \text{where}\, p\,\text{is a prime}, \alpha\in\Bbb N\)