MTH 231

Section 5.1Representations of Integers

Overview

• The integers are an extension of the whole numbers (which, if you will recall, were an extension of the natural numbers).

• Integers (in particular negative integers) have several real-world applications: temperatures below zero, elevations below sea level, overdrawn bank accounts, golf scores, yardage in football.

• Further, we will show that the integers are closed under subtraction (something we could not say about the whole numbers).

• Finally, we will look at several way to model integers.

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The Integers

• The set of integers is made up of:1.The set of whole numbers, and2.Their additive inverses.• We know about the set of whole numbers,

but what about this “additive inverse” thing?

Additive Inverses• Given an integer a, an integer b is the additive

inverse of a if:1. a and b are the same distance from 0 on the

number line, and2. a + b = 0.• The additive inverse of a is usually more

commonly referred to as the opposite of a, and –a is used instead of b.

• The concept of “distance from 0” is later re-introduced as absolute value.

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Ways To Represent Integers

• Colored Counters• Number Line

Colored Counters

• Use two different colors, one to represent positive integers and the other to represent negative integers.

Number Line and Absolute Value

• 0 is in the “center”• Positive integers are to the right of 0.• Negative integers are to the left of 0.• We use absolute value notation, | |, to

denote the distance an integer is from 0 on the number line.

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