Number Systems

Number sets

• N : Natural numbers {0, 1, 2, 3, ... }. Also informally referred to as "whole" numbers, or "counting" numbers (without zero).
• Z: Integers {...-3, -2, -1, 0, 1, 2, 3, ... }. Natural numbers and their negatives.
• Q: Rational numbers. Can be written in the form p/q (q not 0). They are fractions (also include N because they can be written as N/1) [Remember Q for Quotient]
• Q': Irrational numbers (not rational). The decimal form does not terminate or repeat. Common examples are pi and √2.
• R: Real numbers. Includes rational and Irrational numbers.

How to find rational numbers between two numbers?

• Example:
• Find 6 rational numbers between 2 and 3.
• Method 1:
• Write equivalent fractions with a denominator of 7 (6+1).
• 2= 14/7
• 3 =21/7
• Answer:
• {15/7,16/7,17/7,18/7,19/7,20/7}
• Method 2:
• 2.1 = 2+1/10 = 21/10
• etc
• NOTE: There are actually infinitely many rational numbers between 2 & 3!!!
• 
• Caption: Another method is to convert decimals.