#### Mathematical English Usage - a Dictionary

##### by Jerzy Trzeciak

## what

Under those conditions, what does the sum on the left
hand side of (8) signify?

Does the limit of f(z) exist as z goes to zero? If so, what is
it?

What is F(c) if c is a positively oriented circle?

What relation exists between f and g?

By what has been proved, there exists n such that......

What is left is to show that......

What is still lacking is an explicit description of ker C.

Here is a more explicit statement of what the theorem asserts.

The sum of the depths is at most two-thirds of what it was before.

Throughout what follows, we shall freely use without
explicit mention the elementary fact that......

It is not immediately obvious what this generalization has to be.

We conclude that, no matter what the class of b is, we have an
upper bound on M.

But if E is not reflexive or---what is the same---w is weak, then......

Here G is discontinuous and, what is more, it does not belong to V.

[Note the difference between * what* and * which* in sentences similar to
the last two examples: * what* refers to what follows it, while * which* refers
to what precedes it.]

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