Prove or disprove:
Ifis a null sequence then one or both of
is(are) null.
My attempt:
ifboth are null then certainly
is null, no problem with that.
I assumed thatis not null,
is not null and as given,
is null. I tried to bring a contradiction since i have a feeling that the statement in the question is true.
since its assumed thatis not null so:
there existssuch that for all
there exists
such that
similarly:
there existssuch that for all
there exists
such that
and sinceis null:
there existssuch that
now since i can't say thatoccur at the same
i can't find a contradiction.
someone help.