/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 6 Determine if each statement is t... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 6

Determine if each statement is true or false. Every natural number is a whole number.

Short Answer

Expert verified
The statement "Every natural number is a whole number" is true, as every natural number is indeed a whole number, with the only difference between the two sets being the absence of zero in the set of natural numbers.

Step by step solution

01

Understand the statement

For this exercise, we need to determine if the following statement is true or false: "Every natural number is a whole number."
02

Analyze the relationship between natural and whole numbers

Since natural numbers do not include zero, but every other whole number is included in the set of natural numbers. The natural numbers are just the whole numbers without zero.
03

Compare the two number sets

We know that natural numbers are all whole numbers except for zero. So, given that every natural number is a whole number (except for zero), we can conclude that the statement is true.
04

Conclusion

The statement "Every natural number is a whole number" is true. Every natural number is indeed a whole number, with the only difference between the two sets being the absence of zero in the set of natural numbers.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Whole Numbers
Whole numbers are a fundamental part of mathematics. They include all non-negative numbers without any fractions or decimals. This means that whole numbers start from zero and continue to infinity. They look like this:
  • 0, 1, 2, 3, 4, 5, and so on.
Knowing what whole numbers are helps us categorize and understand different sets of numbers. When studying numbers, it's important to remember that zero is included in whole numbers, even though it doesn't appear in some other sets.
Number Sets
In mathematics, we often group numbers into collections known as sets. Each set follows specific rules about which numbers it contains. Some common number sets are:
  • Natural Numbers: This set includes all positive counting numbers like 1, 2, 3, and so forth. It does not include zero or any negative numbers.
  • Whole Numbers: As mentioned, these include all natural numbers but also include zero.
  • Integers: This set expands whole numbers to include negative numbers, like -3, -2, -1, 0, 1, 2, and so on.
  • Rational Numbers: These numbers can be expressed as fractions or ratios between integers.
Understanding these sets is crucial because it allows us to see how different types of numbers relate to and differ from one another.
Mathematical Concepts
Mathematical concepts are the ideas and rules that help us solve problems and understand the world of numbers. These concepts form the foundation of mathematics. Two key concepts are:
  • Relationships Between Sets: Many mathematical problems involve understanding how different sets relate to each other. For example, knowing that natural numbers are a subset of whole numbers is essential for solving some problems.
  • Logical Reasoning: This allows us to figure out whether mathematical statements are true or false by analyzing relationships and drawing conclusions based on given information.
By mastering these concepts, students can improve their problem-solving skills and better understand mathematical exercises.
True or False Statements
Determining whether a statement is true or false is an important skill in mathematics. This involves assessing the accuracy of a claim based on known information and logical reasoning. For instance, consider the statement: "Every natural number is a whole number." To decide whether it's true or false, one needs to understand that:
  • Natural numbers include 1, 2, 3, and onwards.
  • Whole numbers include all natural numbers plus zero.
Since all natural numbers appear in the set of whole numbers, the statement is true. Practicing true or false assessments helps students develop their logical reasoning and deepen their understanding of mathematical relationships.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Write an expression for each and simplify. Answer the question with a complete sentence. The world's tallest mountain, Mt. Everest, reaches an elevation of \(29,028\) ft. The Mariana Trench in the Pacific Ocean has a maximum depth of \(36,201 \mathrm{ft}\) below sea level. What is the difference between these two elevations?

Write an expression for each and simplify. Answer the question with a complete sentence. The bar graph shows the estimated population of Oakland, California, from 2000 to \(2003 .\) Use a signed number to represent the change in Oakland's population over the given years. CAN'T COPY THE TABLE a) \(2000-2001\) b) \(2001-2002\) c) \(2002-2003\)

Write a mathematical expression for each and simplify. The quotient of 63 and \(-9\) increased by 7

Write a mathematical expression for each and simplify. Twice the sum of 18 and \(-31\)

Determine whether each statement is true or false. For any real numbers \(a\) and \(b\).
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.