These guys are the real deal. The real numbers are broken into two groups: the rational numbers and the irrational numbers. But the rational numbers include three other subsets as well: the natural numbers, whole numbers, and integers.
That means the real numbers include the natural numbers, whole numbers, integers, rational numbers, and irrational numbers. Selfish much?
Example 2
Which subsets of the real numbers include -5?
The integers include all whole numbers and their opposites. In other words, they include the negative numbers.
The integers are also included as a subset of the rational numbers, so our answer is technically integers and rational numbers.
Example 3
The number is a nonterminating and nonrepeating decimal. Which subset of numbers is it included in?
"Nonterminating" means a decimal that never ends, like π. "Nonrepeating" means a decimal with no pattern of numbers that repeats on and on forever.
The rational numbers include only decimals that either eventually end or continue forever but with a repeating pattern, such as 0.5, 0.8925983 or 0.34343434…
Because does not end (nonterminating) and does not repeat a pattern (nonrepeating), it's an irrational number. Here are the first million digits of the square root of 7, in case you're curious.
is a nonterminating and nonrepeating decimal. Which subset of numbers is it included in?
does not end (nonterminating) and does not repeat a pattern (nonrepeating), it's an irrational number. Here are the