Cannot understand the sequence definition of the limit sup of a sequence ($a$n) How can we say that $a$n < Lim sup + € except finitely many terms ( Why cant we say that $a$n< lim sup +€ for infinitely many terms?) Also we are saying that $a$n> lim sup -€ for infinitely many terms.(why Cant we say that $a$n > lim sup -€ except finitely many terms ?) Does the two definition hold for every €> 0 ?
2026-03-26 11:16:47.1774523807
Sequence definition of Limit Sup
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'for infinitely many terms' is weaker than 'except finitely many terms'. For instance, a interger is odd for infinitely many intergers, but not except finitely many; a natural number is greater than 5 except finitely many numbers.