Set

:This article is about sets in mathematics. For other senses, see set (disambiguation).

Special sets

There are some sets which hold great mathematical importance and are referred to with such regularity that they have acquired special names to identify them. One of these is the empty set. Some special sets of numbers include:

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• $mathbb\{N\}$ denotes the set of all natural numbers. That is to say, $mathbb\{N\}$ = {1, 2, 3, ...}, or sometimes $mathbb\{N\}$ = {0, 1, 2, 3, ...}.
• $mathbb\{Z\}$ denotes the set of all integers (whether positive, negative or zero). So $mathbb\{Z\}$ = {..., -2, -1, 0, 1, 2, ...}.
• $mathbb\{Q\}$ denotes the set of all rational numbers (that is, the set of all proper and improper fractions). So, $mathbb\{Q\}$ = { : a,b $in\; mathbb\{Z\}$ and b ≠ 0}. For example, and . All integers are in this set since every integer a can be expressed as the fraction .
• $mathbb\{R\}$ is the set of all real numbers. This set includes all rational numbers, together with all irrational numbers (that is, numbers which can't be rewritten as fractions, such as $pi,$ –$pi$ and √2).
• $mathbb\{C\}$ is the set of all complex numbers.

Each of these sets of numbers has infinite cardinality, and moreover mathbb{N} subset mathbb{Z} subset mathbb{Q} subset mathbb{R} subset mathbb{C}.

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