#### Mathematical English Usage - a Dictionary

##### by Jerzy Trzeciak

## fact

[*see also*: information, detail, evidence, proof, actually, more

A stronger result is in fact true.

We note that H is in fact not Lipschitz continuous if this condition
is violated.

In fact, we can do even better, and prescribe finitely many derivatives at
each point of A.

Now, just the fact that F is a homeomorphism lets us prove that......

The advantage of applying...... lies in the fact that......

Observe that (1) just uses the fact that m is unary. [*Not*: “uses that m is unary'']

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