#### Mathematical English Usage - a Dictionary

##### by Jerzy Trzeciak

## lower

**1**

[*see also*: decrease, diminish, reduce]
The importance of these examples lay not only in lowering the
dimension of known counterexamples, but also in...... [Note that the
past tense of * lie* is * lay*, not “lied''.]

**2**

The lower limit is defined analogously: simply interchange sup and inf in (1).

The reader may wonder why we have apparently ignored the possibility
of obtaining a better lower bound by considering......

a path obtained by going from A to B along the lower half of
the circle

a lower semicontinuous function

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