Mathematical English Usage - a Dictionary

by Jerzy Trzeciak


[see also: follow, entail

Then x=y and y=z implies x=z. [Or: imply]

Note that M being cyclic implies F is cyclic.

However, if B were omitted in (1), the case n=0 would imply Nf=1, an undesirable restriction.

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

That (2) implies (1) is contained in the proof of Theorem 1 of [4].

The continuity of f implies that of g.

The implied constants depend on r.

The equivalence of (a) and (b) is trivially implied by the definition of M.

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