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Chapter 1: Problem 2

Describe each set of numbers. Whole numbers

Short Answer

Expert verified
Whole numbers are all the natural numbers including zero. They go from zero to positive infinity, comprising numbers without fractions, decimals, and negative values.

Step by step solution

01

Definition of Whole Numbers

Whole numbers are all of the natural numbers (or positive integers) including zero. This means all numbers {0, 1, 2, 3, 4, 5...} are whole numbers. They are numbers without fractions or decimals, and are all positive or zero.
02

Example of Whole Numbers

Examples of whole numbers include 0, 7, 15, 100, and 2023 among many others. Each of these numbers is a non-negative, non-decimal, non-fractional number.
03

Contrast to Other number sets

In contrast, numbers like -5, 0.75, or 鈭�2, are not whole numbers. -5 is negative, 0.75 is a decimal (or fraction), and 鈭�2 is irrational (not expressible as a simple fraction). Whole numbers are simple, positive numbers, including zero, with no fractional or decimal parts.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Number Sets
Number sets are categories we use to classify different types of numbers based on their characteristics. Understanding these sets is essential as it helps to determine how numbers can be used and manipulated in mathematical operations. Here's a quick overview:
  • Natural Numbers: These include all positive integers starting from 1, such as 1, 2, 3, and so on.
  • Whole Numbers: These are similar to natural numbers, but they also include 0. Thus, they are 0, 1, 2, 3, and so forth.
  • Integers: This set includes both positive and negative whole numbers, in addition to zero. For example, ..., -3, -2, -1, 0, 1, 2, 3...
  • Rational Numbers: These are numbers that can be expressed as a fraction of two integers, such as 1/2 or -3/4.
  • Irrational Numbers: These cannot be expressed as a simple fraction, such as 蟺 or 鈭�2.
These sets build upon each other, starting from natural numbers and expanding step by step.
Natural Numbers
Natural numbers are the simplest number set used in basic counting. They begin from 1 and move onwards to infinity without including zero or negative numbers. These numbers:
  • Are the numbers we first learn to count from: 1, 2, 3, 4, 5...
  • Are used for simple arithmetic operations such as addition and multiplication.
  • Are always whole (no fractions or decimals).
A key thing to remember is that natural numbers are always positive and form the foundation of more complex sets like whole numbers and integers. They are very practical in everyday life, such as counting objects or measuring quantities.
Integers
Integers expand upon whole numbers by including their negative counterparts. So, while whole numbers are just non-negative numbers including zero, integers encompass all of these plus negative numbers:
  • An integer set includes: ..., -3, -2, -1, 0, 1, 2, 3 ...
  • They do not include fractions or decimals 鈥� fully whole numbers only.
  • Useful in various mathematical concepts, including subtraction, where results can be negative.
In summary, integers provide a broader category that includes zero, positive numbers, and negative numbers. They allow for more flexibility in arithmetic operations, especially in contexts where quantities can decrease below zero, such as temperatures or financial debts.

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