Thread: analysis question

1. For some ε > 0 there exists an index N such that
if n > N then absolute value of an- a < ε

2.For each ε > 0 and each index N if n > N then absolutue value an-a <ε
3.There exists an index N such that for all ε > 0 if n > N then absolute value an-a < ε
4. For each ε > 0 and each index N if n > n then absolute value an-a<ε




Match from 1-4

a) The sequence {an} is bounded
b) The sequence {an} is a constant
c) All except finitely many terms of the sequence {an} are equal to constant a
d) Such a sequence does not exist
e) The assertion holds for every sequence

Originally Posted by wvlilgurl

1. For some ε > 0 there exists an index N such that
if n > N then absolute value of an- a < ε

2.For each ε > 0 and each index N if n > N then absolutue value an-a <ε
3.There exists an index N such that for all ε > 0 if n > N then absolute value an-a < ε
4. For each ε > 0 and each index N if n > N then absolute value an-a<ε

4. The sequence is constant since we may let , then it asserts that for all , which implies that for all .

CB