Limits and Continuity

Question 1

Definition of Sequence

Answer 1

A function whose domain is the set N. The nth term of the sequence is the value of the function at n.

Question 2

Definition of limit for sequences

Answer 2

For a sequence <X_n> and a real number L, "the limit of <Xn> is L" means: (for all epsilon >0)(there exists a natural number N)(for all natural numbers m)(m > N -> |X_m - L| < epsilon).</Xn></X_n>

For every positive number epsilon, we can find a positive integer N such that every term of the sequence after the Nth term is within e of L.