# Math of English

## 加减乘除表达

1. $+$ : plus
2. $-$ : minus
3. $\times$ : times or multiplied by
4. $\div$ : divided by
5. $=$ : equals or is equal to

$25+6-8\times7\div3$ : twenty five plus six minus 8 times (multiplied by) 7 divided by three.

1. $>$ : greater than
2. $<$ : less than
3. $\approx$ " approximately equal to

### 分数的表达

1. 分母为2或4: half(2), quarter(4)
2. 一般情况: 基数词/序数词
3. 分子大于1, 则分母用序数词的复数
4. 带分数(mixed fraction),整数和分数之间加上and
5. 分母是十位数以上,且最后为1或2, 分数线用over,且分母用基数词
6. 分子分母很大, 用上面的方法.
7. 代数里面分数用 over
8. 100为分母, 使用 percent
1. $\frac{1}{2}$ one (a) half $\frac{1}{4}$ one quarter

2. $\frac{1}{3}$ one third $\frac{1}{25}$ one twenty-fifth

3. $\frac{2}{3}$ two thirds $\frac{2}{25}$ two twenty-fifths

4. $3\frac{3}{4}$ three and three fourths

5. $\frac{5}{21}$ five over twenty one

6. $\frac{1}{2361}$ one over two thousand three hundred and sixty one

7. $\frac{(2a-1)}{ax+b}$ two a minus 1 over a x plus b

8. $\frac{12}{100}$ twelf percent

### 乘方和乘方根

1. 指数为2: squared
2. 指数为3: cubed
3. 其余指数: to the fourth (power) or the fourth power of
4. 指数为负数: to the minus
5. 根号2: the squared root of
6. 根号3: the cubed root of
7. 其他根号: the sixth root of

$3^2+4^2$ three squared plus four cubed

$a^5$ a to the fifth or the fifth power of a

$x^{-10}$ to the minus tenth power of x

$\sqrt[4] {x^5}$ the fourth root of the fifth power of x

### 集合公式

1. $A \cap B$: the intersection of A and B
2. $A \cup B$: the union of A and B
3. $x\in R$: x is a number of R or x is in R
4. $A \subseteq B$ or $B \supseteq A$: A is a subset of B
5. $A \subset B$ or $B \supset A$: A is a proper subset of B or A is properly included in B
6. $A \rightarrow B$: if A then B
7. $\alpha \Rightarrow \beta$ or $\alpha \rightarrow \beta$: $\alpha$ implies $\beta$ or if $\beta$ then $\alpha$.
8. $A \Leftrightarrow B$ or $A \leftrightarrow B$: A is equivalent to B or A holds if and only if B holds
9. $\varnothing$: empty set or fai
10. $\wedge$: and
11. $\vee$: or
12. $A \wedge B$: the conjunction of A and B or A and B
13. $A \vee B$: the disjunction of A and B or A or B
14. veen diagrams: 韦恩图,集合论使用的图
15. membership table: 成员表,真值表
16. finite and infinite: 注意发音/'fainait/ /'infinit/

### 函数公式

${\color{Red} f}$

### 发音注意

finite 英 ['faɪnaɪt] infinity 英 [ɪn'fɪnɪtɪ] infinite 英 ['ɪnfɪnət]

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