Mathematical English Usage - a Dictionary

by Jerzy Trzeciak


[see also: have to, necessarily, force

Any algorithm to find max must do at least n comparisons.

We must have Lf=0, for otherwise we can replace f by f-Lf.

Our present assumption implies that the last inequality in (8) must actually be an equality.

If there are to be any nontrivial solutions x then any odd prime must satisfy...... In outline, the argument follows that of the single-valued setting, but there are several significant issues that must be addressed in the n-valued case.

Nevertheless, in interpreting this conclusion, caution must be exercised because the number of potential exceptions is huge.

Theorem 3 may be interpreted as saying that A=B, but it must then be remembered that......

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