# Definition:Null Sequence/Analysis

< Definition:Null Sequence(Redirected from Definition:Null Sequence (Analysis))

Jump to navigation
Jump to search
## Definition

### Complex Numbers

Let $\sequence {z_n}$ be a sequence in $\C$ which converges to a limit of $0$:

- $\displaystyle \lim_{n \mathop \to \infty} z_n = 0$

Then $\sequence {z_n}$ is called a **(complex) null sequence**.

### Real Numbers

Let $\sequence {x_n}$ be a sequence in $\R$ which converges to a limit of $0$:

- $\displaystyle \lim_{n \mathop \to \infty} x_n = 0$

Then $\sequence {x_n}$ is called a **(real) null sequence**.

### Rational Numbers

Let $\sequence {x_n}$ be a sequence in $\Q$ which converges to a limit of $0$:

- $\displaystyle \lim_{n \mathop \to \infty} x_n = 0$

Then $\sequence {x_n}$ is called a **(rational) null sequence**.