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Chapter 0: Problem 2

\(\mathbb{W}=\\{0,1,2,3, \ldots\\}\) is called the set of _____ numbers.

Short Answer

Expert verified
whole numbers

Step by step solution

01

Understand the Problem

Identify the pattern and characteristics of the given set \(\backslashmathbb{W} = \{0, 1, 2, 3, \ldots\}\). Note that it is a sequence of numbers starting from 0 and increasing by 1 each time.
02

Recognize the Sequence Type

Observe that the sequence includes 0 and all positive integers. This allows us to classify the set based on mathematical definitions.
03

Identify the Set Definition

Recall the definition of 'whole numbers'. Whole numbers are all non-negative integers, which include 0 and all positive integers: 0, 1, 2, 3, and so on.
04

Conclusion

Given the characteristics and definitions observed, the set \( \backslashmathbb{W} \) is concluded to belong to the category of 'whole numbers'.

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Key Concepts

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

whole numbers
In mathematics, **whole numbers** refer to a set of non-negative integers starting from zero and increasing by one unit at a time. This means the sequence begins at 0 and includes numbers like 1, 2, 3, and so forth. The concept of whole numbers is fundamental as it represents numbers without fractions or decimals, simplifying arithmetic operations. For instance, counting objects or measuring discrete quantities often involves whole numbers, making them indispensable in daily life and various mathematical applications.
mathematical sequence
A **mathematical sequence** is an ordered list of numbers where each number is related to its predecessor by a specific rule. In the given context, the set \(\backslashmathbb{W} = \{0, 1, 2, 3, \ldots\}\) forms a simple sequence. Each subsequent number increases by one. Understanding sequences is vital because they lay the foundation for more complex mathematical concepts such as series, progressions, and patterns. Sequences help in recognizing and predicting trends or behaviors in various scientific and real-world scenarios.
non-negative integers
The term **non-negative integers** refers to all whole numbers starting from zero and moving upwards indefinitely. This set includes 0, 1, 2, 3, and so forth. Non-negative integers do not include negative numbers or fractions. They are used frequently in scenarios where only whole unit measurements are meaningful, like in counting items, population studies, or inventory. Recognizing non-negative integers is essential because they are a subset of integers and provide a foundation for various branches of mathematics, including number theory and statistics.

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Most popular questions from this chapter

Determine the sign of the expression. Assume that \(a, b,\) and \(c\) are real numbers and \(a<0, b>0,\) and \(c<0\). $$\frac{b(a+c)^{3}}{a^{2}}$$

Write an inequality representing the given statement. \(a\) is not positive.

Add or subtract as indicated and simplify. $$ \left(0.05 c^{3} b+0.02 c^{2} b^{2}-0.09 c b^{3}\right)-\left(-0.03 c^{3} b+0.08 c^{2} b^{2}-0.1 c b^{3}\right) $$

Multiply and simplify. $$ (w+7)(6 w-3) $$

Perform the indicated operations and simplify. $$ (3 p-2)(3 p+2) $$
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