Begin sentences with word, not math symbol.
$A$ is a subset of $B$. ❌
The set $A$ is a subset of $B$. ✔️
$x^2 - x + 2 = 0$ has two solutions. ❌
The equations $x^2 - x + 2 = 0$ has two solutions. ✔️
End each sentence with a period, even when it ends with math symbol or expression.
- Euler proved that $\sum_{k=1}^{\infty}\frac{1}{k^{s}}=\prod_{p\in P}\frac{1}{1-\frac{1}{p^{s}}}$ ❌
- Euler proved that $\sum_{k=1}^{\infty}\frac{1}{k^{s}}=\prod_{p\in P}\frac{1}{1-\frac{1}{p^{s}}}$. ✔️
Separate math symbols and expressions with words.
- Because $x^2 - 1 = 0$, $x = 1$ or $x = -1$. ❌
- Because $x^2 - 1 = 0$, it follows that $x = 1$ or $x = -1$. ✔️
Avoid misuse of symbols
The empty set is a $\subset$ of every set. ❌
The empty set is a subset of every set. ✔️
Since $a$ is odd and $x$ odd $\implies x^2$ odd, $a^2$ is odd. ❌
Since $a$ is odd and and any odd number squared is odd, $a^2$ is odd. ✔️
Avoid using unnecessary symbols.
- No set $X$ has negative cardinality. ❌
- No set has negative cardinality. ✔️
Explain each new symbol.
- Since $a|b$, it follows that $b = ac$. ❌
- Since $a|b$, it follows that $b = ac$ for some integer $c$. ✔️
Watch out for “it”.
- Since $X \subset Y$, and $0 \lt |X|$, we see that it is not empty. ❌
- Since $X \subset Y$, and $0 \lt |X|$, we see that $Y$ is not empty. ✔️