Mathematically, set of integer numbers are denoted by blackboard-bold(**ℤ**) form of “Z”. And the letter “Z” comes from the German word **Zahlen**(numbers).

Blackboard-bold is a style used to denote various mathematical symbols. For example natural numbers, real numbers, whole numbers, etc.

In latex, the \mathbb command is used to convert a latter to blackboard-bold form, and the latter is passed as an argument in the command.

And this \mathbb command is included in more than one package. For example

amsfonts | `\mathbb{Z}` → |

amssymb | `\mathbb{Z}` → |

txfonts | `\mathbb{Z}` → |

pxfonts | `\mathbb{Z}` → |

```
\documentclass{article}
\usepackage{amsfonts}
\begin{document}
\[ \mathbb{Z}\subset\mathbb{Q}\]
\[ \mathbb{Z}=\{\ldots,-2,-1,0,1,2,\ldots\} \]
\end{document}
```

**Output :**

Integer number sets are divided into different parts depending on the positive and negative and those parts are denoted by different symbols.

## Positive integer symbol

Positive integer symbols have been identified in different ways by different authors in different books. E.g. **ℤ ^{+}**,

**ℤ**, and

_{+}**ℤ**.

^{>}```
\documentclass{article}
\usepackage{amsfonts}
\begin{document}
\[ \mathbb{Z}^{+}=\{1,2,3,\ldots\} \]
\[ \mathbb{Z}_{+}=\{1,2,3,\ldots\} \]
\[ \mathbb{Z}^{>}=\{1,2,3,\ldots\} \]
\end{document}
```

**Output :**

## Non-negative integer symbol

The second is the non-negative integer which includes all the positive numbers including zero. And which is denoted by **ℤ**^{0+} and **ℤ ^{≥}** symbols.

```
\documentclass{article}
\usepackage{amsfonts}
\begin{document}
\[ \mathbb{Z}^{0+}=\{0,1,2,3,\ldots\} \]
\[ \mathbb{Z}^{\geq } =\{0,1,2,3,\ldots\} \]
\end{document}
```

**Output :**

## Non-zero integer symbol

And the third is the non-zero integer denoted by the** ℤ ^{≠}** and

**ℤ**symbols.

^{*}```
\documentclass{article}
\usepackage{amsfonts}
\begin{document}
\[ \mathbb{Z}^{\neq}=\mathbb{Z}-\{0\} \]
\[ \mathbb{Z}^{*} =\{\dots,-2,-1,1,2,\ldots\} \]
\end{document}
```

**Output :**

Hopefully, this tutorial has been presented to you in a very simple way. Even after this, if you have any difficulty in understanding, don’t forget to comment. Thank you