#### Mathematical English Usage - a Dictionary

##### by Jerzy Trzeciak

## do

[cf. make

We shall do this by showing that......

This is done to simplify the notation.

As the space of Example 3 shows, complete regularity of X is not enough to allow us to do that.

For binary strings, the algorithm does not do quite as well.

Recent improvements in the HL-method enable us to do better than this.

In fact, we can do even better, and prescribe finitely many derivatives at
each point of M.

A geodesic which meets bM does so either transversally or......

We have not required f to be compact, and we shall not do so except when
explicitly stated.

This will hold for n>1 if it does for n=1.

Consequently, A has all geodesics closed if and only if B does.

We can do a heuristic calculation to see what the generator of x_{t}
must be.

In contrast to the previous example, membership of D(A) does impose
some restrictions on f.

We may (and do) assume that......

The statement does appear in [3] but there is a simple gap in the
sketch of proof supplied.

Only for x=1 does the limit exist.

In particular, for only finitely many k do we have F(a_{k})>1.
[Note the inversion after * only.*]

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