#### Mathematical English Usage - a Dictionary

##### by Jerzy Trzeciak

## into

We must now bring dependence on d into the arguments of [9].

The proof will be divided into a sequence of lemmas.

We can factor g into a product of irreducible elements.

Other types fit into this pattern as well.

This norm makes X into a Banach space.

We regard (1) as a mapping of S^{2} into S^{2}, with the obvious
conventions concerning the point ∞.

We can partition [0,1] into n intervals by taking......

The map F can be put <brought> into this form by setting......

The problem one runs into, however, is that f need not be......

But if we argue as in (5), we run into the integral......, which is meaningless as it stands.

Thus N separates M into two disjoint parts.

Now (1) splits into the pair of equations......

Substitute this value of z into <in> (7) to obtain......

Replacement of z by 1/z transforms (4) into (5).

This can be translated into the language of differential forms.

Implementation is the task of turning an algorithm into a computer
program.

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