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 g1,...,gn without common zero.

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



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