#### Mathematical English Usage - a Dictionary

##### by Jerzy Trzeciak

## idea

[*see also*: concept, notion, objective, definiteness

Some of the basic ideas from functional analysis are also included.

The main idea of the proof is to take......

The idea behind our use of the map σ is that......

The idea is to relax the constraint of being a weight function
in Theorem 3.

It is this idea that underlies some of the results of [2].

This idea goes back at least as far as [3].

Apart from a few embellishments necessitated by some technical difficulties, the ideas differ very little from those used to prove Lemma 4.

Our proof of Theorem 2 is based upon ideas found in [BN].

The proof makes use of many of the ideas of the general case, but in
a simpler setting.

Although the idea is simple, its implementation is complicated by the fact that......

It is a pleasure to thank R. Greenberg for bringing his criterion
for...... to our attention, and for generously sharing his ideas about
it.

We shall draw heavily on ideas from [3].

To fix ideas, assume that M is a pentagon.

a stimulating <clever/original/alternative/basic> idea

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