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In this post, we will study several important examples of set. The elements of these sets are all numbers. Notations are:

$\mathbb{N}$: Natural numbers.

$\mathbb{Z}$: Integers.

$\mathbb{Q}$: Rational numbers.

$\mathbb{R}$: Real numbers.

$\mathbb{N} \subset \mathbb{Z} \subset \mathbb{Q} \subset \mathbb{R}$.

Also, assume the addition (加法) and multiplication (乘法) of integers, i.e., $1+1=2, 3-5=-2, 4 \cdot (-2)=-8$. Now we can start to develop these number systems (sets).

1. Natural numbers

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