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Rational, Irrational, and Real Numbers
Introduction
to numbers:
- Natural Numbers: N = {1, 2, 3, 4, 5, 6,
…}
- Whole Numbers: W = {0, 1, 2, 3,
4, 5, 6, …}
- Integers: I = { …, -5, -4, -3, -2,
-1, 0, 1, 2, 3, 4, 5, …}
 | Positive integers are {1, 2, 3, 4, 5, 6, … } |
| Negative integers are {-1, -2, -3, -4, -5, … }
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| Non-negative integers are {0, 1, 2, 3,
4, 5, … } |
| Non-positive integers are {0, -1, -2,
-3, -4, -5, …< } |
Rational Numbers, Q, are all
the numbers that can be written as a/b where a and b are integers and b can't be zero. A decimal number that terminates or repeats is also a rational
number. Any real number that is not a
rational number is an irrational number.
Real Numbers: R is the combination of all
rational and irrational numbers.
The following is a
breakdown of the number system
Real numbers (combination of
rational and irrational)
 | Irrational numbers |
| Rational Numbers (combination of fractions and integers) |
| Fractions (Non-integer) |
| Integers (combination of whole numbers and negative integers) |
| Negative integers |
| Whole numbers (combination of zero and natural numbers) |
| Natural numbers |
| Zero |
Subsets of the
Rational Numbers:
| Natural numbers are a subset of rational numbers:  |
| Whole numbers are a subset of rational numbers:  |
| Integers are also rational numbers:  |
Example:
True or False.
Example:
Classify each of the following decimal numbers as being either rational or irrational.
Multiplicative
Inverse or Reciprocal:
The multiplicative inverse of any number (except zero) is the reciprocal of that
number. The mult. inv. of a number is equal to 
Example 3:
To find the mult. inv. of a fraction, just flip the fraction.
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