## Mathematical English Usage - a Dictionary

## first

#### 1

[*see also*: original]

He was the first to propose a complete theory of triple intersections.

Because N. Wiener is recognized as the first to have constructed such a measure, the measure is often called the Wiener measure.

Let $S_i$ be the first of the remaining $S_j$.

The first two are simpler than the third. [*Or*: the third one; * not*: “The first two ones”]

As a first step we shall bound $A$ below.

We do this in the first section, which the reader may skip on a first reading.

At first glance, this appears to be a strange definition.

The first and third terms in (5) combine to give ......

the first author = the first-named author

#### 2

[*see also*: initially, originally, beginning, firstly]

First, we prove (2). [*Not*: “At first”]

We first prove a reduced form of the theorem.

Suppose first that ......

His method of proof was to first exhibit a map ......

In Lemma 6.1, the independence of $F$ from $V$ is surprising at first.

It might seem at first that the only obstacle is the fact that the group is not compact.

[Note the difference between * first* and * at first*: * first* refers to something that precedes everything else in a series, while * at first* [= initially] implies a contrast with what happens later.]

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