# analysis question

• Feb 20th 2009, 11:17 AM
wvlilgurl
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
• Feb 21st 2009, 01:26 AM
CaptainBlack
Quote:

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 $N=1$, then it asserts that for all $\varepsilon>0$ $:|a_n-a|<\varepsilon$, which implies that for all $n\ge1:\ a_n=a$.

CB