#### Mathematical English Usage - a Dictionary

##### by Jerzy Trzeciak

## the

Note that the P produced in Theorem 2 need not have dP=0.

......where the P_{k} are polynomials.

We characterize the Banach spaces X for which n(X)=1.

Thus π_{n}(X) can be interpreted as the homotopy classes of maps
S^{n}→ X. [= as the set of * all* homotopy classes]

It has some basic properties in common with another most important class of
functions, namely, the continuous ones.

In the plane, the open sets are those which are unions of open circular
discs.

the number of zeros of f in D

the density of the zeros of f

Let A be the union of the sets f(Q) for f in F.

Here p_{2}(r) is the sum of the squares of the divisors of r.

The problem has a very natural connection with the problem of the distribution of the zeros of a bounded holomorphic function in a half-plane.

Intuitively, entropy of a partition is a measure of its information
content---the larger the entropy, the larger the information content.

Back to main page