#### Mathematical English Usage - a Dictionary

##### by Jerzy Trzeciak

## every

[*see also*: all, any, each, arbitrary

To every F there corresponds a unique......

For every g in X <not in X> there exists an X......
[* But*: for all f and g, for any two maps f and g;
* every* is
followed by a singular verb.]

Every invariant subspace is of the form......

[Do not write: “Every subspace
is not of the form......” if you mean: * No subspace is of the form*......;
* every*
has to be followed by an affirmative statement.]

However, not every ring enjoys the stronger property of being bounded.

Every possible such sequence gives rise to......

The generally accepted point of view in this domain of science seems to be
changing every few years.

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