## Mathematical English Usage - a Dictionary

## both

[*see also*: either]

Both $f$ and $g$ are obtained by ...... [*Or*: $f$ and $g$ are both obtained]

For both $C^{\infty} $ and analytic categories, ......

Here $C$ behaves covariantly with respect to maps of both $X$ and $G$.

We now apply (3) to both sides of (6).

Both conditions $\langle$Both these conditions/Both the conditions$\rangle$ are restrictions only on ...... [* Note*: * the* after * both.*]

Then $C$ lies on no segment both of whose endpoints lie in $K$.

Two consecutive elements do not belong both to $A$ or both to $B$.

Both its sides are convex. [*Or*: Its sides are both convex.]

Here $B$ and $C$ are nonnegative numbers, not both 0.

Choose points $x$ in $M$ and $y$ in $N$, both close to $z$, such that ......

We show how this method works in two cases. In both, $C$ is ......

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