#### Mathematical English Usage - a Dictionary

##### by Jerzy Trzeciak

## to

The following lemma, crucial to Theorem 2, is also implicit in [4].

Knowing this matrix is equivalent to knowing the multiplicities of the
l_{i}.

Essential to the proof are certain topological properties of G.

We shall see later that the values of h(n) for large n are irrelevant
to the problem.

But the T_{n} need not be contractions in L^{1}, which is the main obstruction to applying standard arguments for densities.

We can join a to b by a path π. [*Not*: “join a with b'']

Exercises 2 to 5 [= Exercises 2--5; * amer.* Exercises 2 through 5]

To deal with (3), consider......

We now apply (2) to get Nf=0.

To see that f=g is fairly easy.

Every prime in the factorization appears to an even power.

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