/*! 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 59 Use roster notation to write eac... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 59

Use roster notation to write each set. The set of all natural numbers that are multiples of 10

Short Answer

Expert verified
\( \{ 10, 20, 30, 40, 50, ... \} \)

Step by step solution

01

Understand the Problem

Identify all natural numbers that are multiples of 10. Recall that natural numbers start from 1 and go up without any upper limit (e.g., 1, 2, 3, ...). A multiple of 10 is any number that can be written as 10n, where n is a natural number.
02

Find Some Multiples of 10

To become familiar with the pattern, write down a few multiples of 10: 10, 20, 30, 40, 50, and so forth. Notice the consistent increase by 10 in each step.
03

Represent the Set in Roster Notation

In roster notation, we list the elements of the set separated by commas, and enclose them in curly braces. Since our set is infinite, we use an ellipsis (...) to indicate that the pattern continues indefinitely.
04

Write the Final Set

The set of all natural numbers that are multiples of 10 can be written as: \[ \text{{Set of multiples of 10}} = \{ 10, 20, 30, 40, 50, ... \} \]

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.

Natural Numbers
Natural numbers are the set of positive integers starting from 1 and going on forever. These numbers are the most fundamental of all, forming the basis for arithmetic and number theory. Here are some key features:
  • They start from 1 and increase without end (e.g., 1, 2, 3, 4, ...).
  • Natural numbers do not include zero or negative numbers.
  • They are used for counting and ordering.
This understanding is crucial when identifying multiples of other numbers, as you will always be dealing with these positive, incrementing values.
Multiples
A multiple of a number is any value that can be expressed as that number times an integer. For instance, the multiples of 10 are all numbers that can be written in the form of 10n, where n is a natural number. Here are some important points about multiples:
  • To find multiples of a number, you simply keep adding the number to itself repeatedly. For example, multiples of 10 are 10, 20, 30, and so on.
  • The multiples form a specific pattern, which in this case is an increase by 10 at each step.
  • In math, discovering multiples helps in many areas like simplifying fractions, finding least common multiples, etc.
Being able to identify and work with multiples is essential for understanding patterns and sequences in mathematics.
Infinite Sets
An infinite set is a collection of elements that has no end or limit. For example, the set of natural numbers, multiples of 10, and many other mathematical constructs are infinite. Here鈥檚 what you need to know about infinite sets:
  • Infinite sets keep growing without a terminating point. This means that you can always find a larger number in the set no matter how far you go.
  • In roster notation, infinite sets are represented with an ellipsis ( ... ) to show that the pattern continues indefinitely.
  • Infinite sets are different from finite sets, which contain a limited number of elements.
Understanding infinite sets is important especially in higher mathematics, as it helps to comprehend the concept of limitless growth and endless sequences.

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

Classify each statement as either true or false. The following sets are used: \(\mathrm{N}=\) the set of natural numbers; \(W=\) the set of whole numbers; \(\mathbb{Z}=\) the set of integers; \(\mathbb{C}=\) the set of rational numbers; \(\mathrm{H}=\) the set of irrational numbers; \(\mathrm{R}=\) the set of real numbers. $$ 196 \in \mathbb{N} $$

Calculate using the rules for order of operations. Are subtraction and division commutative? Why or why not?

Use set-builder notation to write each set. The set of all even numbers between 9 and 99

To the student and the instructor: Throughout this text selected exercises are marked with the icon Ahal. Students who pause to inspect an Ahal exercise should find the answer more readily than those who proceed mechanically. This may involve looking at an earlier exercise or example, or performing calculations in a more efficient manner. Some Ahal exercises are left unmarked to encourage students to always pause before working a problem. Evaluate each expression using the values provided. $$ (m-2 n)^{2}-2(m+n), \text { for } m=8 \text { and } n=1 $$

Which numbers in the list provided are (a) whole numbers? (b) integers? (c) rational numbers? (d) irrational numbers? (e) real numbers?. $$ -8.7,-3,0, \frac{2}{3}, \sqrt{7}, 6 $$
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Applied Mathematics

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.