# Definition:Null Sequence/Analysis

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## 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**.