Mathematical English Usage - a Glossary

by Jerzy Trzeciak

require

[see also: call for, entail, demand, want, desire, necessitate, force, involve]

......, as required <claimed/desired>.

In addition to f being convex, we require that F be holomorphic. [Note the subjunctive be.]

This is equivalent to requiring that......

If (ii) is required for finite unions only, then M is called an algebra of sets.

When clarity requires it, we shall write......

Many of the results that follow only require W to satisfy (8).

The algebraic properties (i) and (ii) required of j are evidently true.

Lemma 3 does not require D to be prime.

The only point that requires care is the verification of......

The projection technique requires the introduction of an appropriate homomorphism.

We will show that V is the required open cover.


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