Mathematical English Usage - a Dictionary

by Jerzy Trzeciak


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

Knowing this matrix is equivalent to knowing the multiplicities of the li.

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 Tn need not be contractions in L1, 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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