#### Mathematical English Usage - a Dictionary

##### by Jerzy Trzeciak

## without

This shows that f could not have n zeros without being identically zero.

Hence Z enters D without meeting x=0.

Thus C can be removed without changing the union.

This allows proving the representation formula without having
to integrate over X.

Take g_{1},...,g_{n} without common zero.

Throughout what follows, we shall freely use without
explicit mention the elementary fact that......

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