# Definition:Null Sequence/Analysis

## Definition

### Complex Numbers

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

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

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 $0$:

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

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 $0$:

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

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