Algebra & Trigonometry 2e

• Mathematics is the language of science
• The earliest use of numbers occurred 100 centuries ago in the Middle East to count, or enumerate items
• Farmers, cattle herders, and traders used tokens, stones, or markers, to signify a single quantity
• Three to four thousands years ago, Egyptians introduced fractions. They first used them to show reciprocals. Later, they used them to represent the amount when a quantity was divided into equal parts
• It was not until about the fifth century CE in India that zero was added to the number system and used as a numeral in calculations
• In India, in the seventh century CE, negative numbers were used as solutions to mathematical equations and commercial debts
• Every natural number, whole number, and integer is a rational number with a denominator of 1
• Natural Numbers are used for counting or enumerating. They are also called Counting Numbers.
• Ellipsis indicates that numbers continue to infinity
• Whole Numbers are a set of natural numbers plus zero
• Integers adds the opposites of the natural numbers to the set of whole numbers
• Rational Numbers include fractions, decimals, natural numbers, whole numbers, and integers.
• Irrational Numbers are numbers that cannot be written as fractions
• Real Numbers are sets of rational and irrational numbers
• Real Numbers include negative, zero, and positive subsets