# 计数方法

• 小数(decimal; decimal number)
0.5: zero point five; point five.
10.875: ten point eight seven five.
• 小数舍入(rounding)
1.2735 rounded to 3 decimal places is 1.274.
• 分数(fraction; fraction number)
a/b: a over b.
1/2: one half.
1/100: one hundredth.
分子: numerator; 分母: denominator.
• 百分数(percentage)
10%: ten percent.
• 科学计数(scientific notation)
$1.23\times10^3$: 1.23 times ten to the power of three; 1.23 times ten to the third (参考幂运算).

# 基本运算

• 四则运算(Elementary arithmetic)
$a+b=c$: a plus b equals c (plus是介词).
$a-b=c$: a minus b equals c (minus是介词); b substracted from a leaves c.
$a\times b=c$: a times b equals c (times是介词); a multiplied by b is c.
$a\div b=c$: a divided by b equals c.
$1/x$: the reciprocal of x.
$3:5$: three to five.
• 乘方/幂运算(exponentiation)
$a^n$: a to the n-th (power); a to the power of n; a raised to the n-th power.
$x^2$: x squared.
$y^3$: y cubed.
指数: exponent.
底数: base.
$\sqrt{9}$: the square root of 9.
$\sqrt[3]{8}$: the cube root of 8.
$\sqrt[n]{b}$: the n-th root of b.
• 对数(logarithm)
$\log_b x$: the logarithm of x to base b.
$\log x,\ \ln x,\ \log_e x$: the natural logarithm of x.
$\lg x,\ \log_{10} x$: the common logarithm of x.
$\text{lb}\ x,\ \log_2 x$: the binary logarithm of x.
• 阶乘(factorial)
5!: five factorial.

# 基本符号

• 小括号() (parentheses)
$(2x - 6y) - 10$: the quantity two x minus six y, close quantity, minus ten;paren, two x minus six y, close paren, minus ten; left paren, two x minus six y, right paren, minus ten.
$a (x - y)$: a, parenthesis, x minus y, close parenthesis.
• 中括号[] (brackets)
• 大括号\{\} (brace)
• 斜线/ (slash)
• 反斜线\\ (backslash)
• 井号# (hash; number sign, pound sign)
• 与号& (ampersand)
a & b: a and b.
• 星号* (asterisk, star)
$x^*$: x star; x asterisk.
• 十字$\dagger$ (dagger)
• 撇号’ (apostrophe)
$a’$: a prime (US); a dash (UK).
$a’’$: a double prime (US); a double dash (UK).
• 省略号$\cdots$ (ellipsis)
$\frac12+\frac14+\frac18+\cdots$: one half plus one quarter plus one eighth and so forth.
• 叹号! (exclamation mark)
• 逗号, (comma)
• 句号. (full stop, period)
• 问号? (question mark)

# 特殊数学符号

• 正负号$\pm$ (plus-minus)
• 成比例$\propto$ (is proportional to)
• 无穷$\infty$ (infinity)
• 上下标 (superscript, subscript)
$a_1$: a (sub) one.
$\varepsilon_{ijk}$: epsilon (sub) ijk.
$a^i$: a super i.
• 附加符号(diacritic)
$\bar{a}$: a bar.
$\tilde{x}$: x tilde.
$\hat{a}$: a hat.
$\dot{y}$: x dot.
$\vec{x}$: vector x.

# 逻辑运算符号

• 相等$=$ (equal, is equal to)
• 不等$\neq$ (is not equal to)
• 大于$>$ (is greater than, is larger than)
• 小于$<$ (is less than, is smaller than)
• 大于等于$\geqslant$ (is greater than or equal to)
• 小于等于$\leqslant$ (is less than or equal to)
• 约等于$\approx$ (is approximately equal to)
• 赋值$:=$ (is set to be, is defined to be)

# 代数与函数运算符号

• 绝对值(absolute value)
• 求和(summation)
$\sum_{k=1}^n k^2$: the summation over k from 1 to n of k squared; the summation of k squared over k from 1 to n.
• 求积(product)
$\prod_{k=1}^n \frac1k$: the product over k from 1 to n of one over k.
• 函数(function)
$f(x)$: f of x.
参数、变量: argument.
• 反函数(inverse function)

# 微积分符号

• 极限(limit)
$\lim_{x\to 0} f(x)$: the limit as x approaches zero of f of x; the limit of f of x as x approaches zero.
• 导数(derivative)
$f’(x)$: f prime of x; the derivative of f with respect to x.
$\frac{dy}{dx}$: d y over d x; the derivative of y with respect to x.
$\frac{\pd y}{\pd x}$: partial y over partial x; d y over d x; the partial derivative of y with respect to x.
• 积分(integral)
$\int_0^\infty f(t)dt$: the integral from t equals 0 to t equals infinity of f of t d t; the integral of f of t d t as t goes from 0 to infinity; integrate f of t d t from 0 to infinity.

# 方程的解

• the solution of equation
• the solution for x
• the key to the question