section_path: Properties/Sequences of real numbers
section_name: Sequences of real numbers
paragraph_text: Sequences of real numbers
  
  For sequences of real numbers, a number of properties can be proven. Suppose { a n } {\displaystyle \{a_{n}\}} and { b n } {\displaystyle \{b_{n}\}} are two sequences converging to a {\displaystyle a} and b {\displaystyle b} respectively.
  
  a n + b n → a + b. {\displaystyle a_{n}+b_{n}\rightarrow a+b.}
  
  a n ⋅ b n → a ⋅ b. {\displaystyle a_{n}\cdot b_{n}\rightarrow a\cdot b.}
  
  1 a n → 1 a. {\displaystyle {\frac {1}{a_{n}}}\rightarrow {\frac {1}{a}}.} Equivalently, the function f (x) = 1 / x {\displaystyle f(x)=1/x} is continuous about nonzero x {\displaystyle x}.