Proposition: Algebra on Convergent Sequences

Suppose and are converging to a and b, respectively. Then
  1. Their sum is convergent to a + b, and the sequences can be added term by term.
  2. Their product is convergent to a * b, and the sequences can be multiplied term by term.
  3. Their quotient is convergent to a / b, provide that b # 0, and the sequences can be divided term by term (if the denominators are not zero).
  4. If an bn for all n, then a b

Proof:

To Theory | Glossary | Map
(bgw)