#### Mathematical English Usage - a Dictionary

##### by Jerzy Trzeciak

## let

Let R be a ring and A a right R-module.

Let f satisfy (2). [*Not*: “Let f satisfies (2)”, nor “Let f verify (2)''.]

Let f be the linear form g→ (m,g).

We let T denote the set of......

One cannot in general let A be an arbitrary substructure here.

Letting m tend to zero identifies this limit as H.

As we let t vary, f(t) describes a curve in M.

The desired conclusion follows after one divides by t and lets t tend to 0.

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

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