#### Mathematical English Usage - a Dictionary

##### by Jerzy Trzeciak

## last

The vector v has at least n ones in its last m positions.

This last result means that......

This last means that......

These last two are called the Banach maps.

(see the last paragraph but one of page 24)

The last but one step is justified by the fact that......

the next-to-last inequality = the second last inequality= the penultimate inequality

the third last row = the antepenultimate row

the last-mentioned map

Now (d) is clear from the very last statement of Theorem 4.

He accounts for all the major achievements in topology over the last few
years.

We can at last show that the limit in (1) exists. [Note that * at last* means “after much delay'';
to introduce a last point or reason, use * finally* or * lastly.*]

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