PEMDAS: Parentheses / Exponentiation / Multiplication and Division / Addition and Subtraction

$\ a + b = c$

  • Terms: $a$ and $b$
  • Sum: $c$
  • Operator: $+$

$\ a - b = c$

  • Difference: $c$

$\ a \times b = a\cdot b = ab = c$

  • Factors: $a$ and $b$
  • Product: $c$

$\ a \div b = a / b = \frac{a}{b} = c$ remainder $d$

  • Dividend/numerator: $a$
  • Divisor/denominator: $b$
  • Quotient: $c$
  • Remainder: $d$

$\ \frac{1}{a} = b$

  • Reciprocal of $a$: $b$

$\ a^b = c$

  • Base: $a$
  • Exponent/power: $b$
  • Product: $c$
  • $b$-th root of $c$: $a$

$\ \log_ab$

  • Base: $a$

$\ ax^2 + bx + c = y$

  • Constants: $a$, $b$, $c$
  • Variables: $x$, $y$
  • Coefficients: $a$, $b$

$\ f(x) = y$

  • Function: $f$
  • Input: $x$
  • Output: $y$
  • Inverse of function $f$: $f^{-1}(x)$
  • Derivative of $f$ (“f prime of x”): $f^{\prime}(x)$
  • Alternative notations for derivative: $f’(x) = \frac{\mathrm{d}f}{\mathrm{d}x} = \frac{\mathrm{d}y}{\mathrm{d}x} = \dot{y}$

Number sets

\[\mathbb{N} \subset \mathbb{Z} \subset \mathbb{Q} \subset \mathbb{R}\]
Symbol Name Examples Closed operations
$\mathbb{N}^* = \mathbb{Z}^+$ Counting numbers $1,2,3$ $+,\times,a^b$
$\mathbb{N}_0 = \mathbb{Z}^{\geq 0}$ Natural numbers $0,1,2,3$ $+,\times,a^b$
$\mathbb{Z}$ Integers $\text{-}3,\text{-}2,\text{-}1,0,1,2,3$ $+,\times,-$
$\mathbb{Q}$ Rational numbers $\text{-}\frac{1}{2},0,\frac{1}{2},0.\bar{7},0.\dot{8},1,3$ $+,\times,-,\div$
$\mathbb{R}$ Real numbers $\text{-}1,0,\frac{1}{2},1,\sqrt{2},2,e,3,\pi$ $+,\times,-,\div$
$\mathbb{C}$ Complex numbers $5+3i, 1+\sqrt{2}i$ $+,\times,-,\div,a^b$
$\mathbb{R} \setminus \mathbb{Q}$ Irrational numbers $\pi, \sqrt{2}, e$  
$\mathbb{C} \setminus \mathbb{R}$ Imaginary numbers $\sqrt{-2},3i$  
$\mathbb{P}$ Prime numbers $2,3,5,7,11,127,2^{31}-1$  
  Undefined functions/operations $\frac{1}{0}, \tan{\frac{\pi}{2}}, \log{0}, \infty, 0^0$