Prove or disprove:
If is a null sequence then one or both of is(are) null.
My attempt:
if both are null then certainly is null, no problem with that.
I assumed that is 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 that is not null so:
there exists such that for all there exists such that
similarly:
there exists such that for all there exists such that
and since is null:
there exists such that
now since i can't say that occur at the same i can't find a contradiction.
someone help.