Mathematical English Usage - a Dictionary

by Jerzy Trzeciak

subsequence

Then we can find a subsequence (still denoted by a_n) such that a_n<1 for all n.

Then we can find a subsequence (not renamed) such that a_n<1 for all n.

Thus every subsequence contains a further subsequence converging weakly to some limit.

Passing to a subsequence if necessary, we can assume that......