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Chapter 1: Problem 19

Determine whether the following statements are true or false. 6 is an integer.

Short Answer

Expert verified
The statement '6 is an integer.' is true.

Step by step solution

01

Understanding Integer

An integer in mathematics is a whole number, either positive, negative or zero. It does not include fractions, decimals, or numbers with imaginary parts.
02

Analyze the Given Statement

The given statement is '6 is an integer.' Here, 6 is a whole number without a fractional or decimal part and it's positive.
03

Conclusion

As 6 fits the definition of an integer, we can conclude that the statement '6 is an integer.' is true.

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Key Concepts

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

Whole Numbers
Whole numbers are a fundamental concept in mathematics. They are the set of numbers that start from zero and include all the positive numbers without any fractions or decimals.
These include numbers like 0, 1, 2, 3, and so on. Whole numbers are part of the larger family called integers, which also include negative numbers.
  • Key feature of whole numbers is that they have no fractional or decimal part.
  • They are used in everyday counting and simple arithmetic operations like addition and subtraction.
By understanding whole numbers, you lay the foundation to grasp more complex mathematical concepts.
Remember, whole numbers form the basis of counting and are the simplest forms of numbers we encounter daily.
Number Classification
Number classification is a critical topic in mathematics which involves organizing numbers into various categories.
It's important for understanding how different numbers relate to each other and their unique properties.
  • Natural Numbers: The set of numbers used for counting which includes 1, 2, 3, etc.
  • Whole Numbers: Includes all natural numbers plus zero.
  • Integers: Encompasses all whole numbers and their negative counterparts, such as -3, -2, -1, 0, 1, 2, 3.
  • Rational Numbers: Numbers that can be expressed as fractions or ratios, like 1/2 or 3/4.
  • Irrational Numbers: Numbers that cannot be written as a simple fraction, such as 鈭�2 or 蟺.
  • Real Numbers: The set that includes both rational and irrational numbers. They represent any point on the number line.
Each classification helps us understand how to solve problems and apply different operations. Knowing these classifications can aid in simplifying equations and comprehending advanced mathematical statements.
Mathematical Statements
Mathematical statements are expressions that can be determined to be true or false.
These statements form the backbone of mathematical reasoning and proofs. They help us establish facts and solve problems using logical thought processes.
  • True Statements: These are facts that hold under the rules of mathematics, like '6 is an integer.'
  • False Statements: These are claims that do not hold, such as stating '6 is a fraction.'
Understanding the truth or falsehood of mathematical statements involves analyzing each term in the statement.
By doing so, you can apply the rules of logic to verify whether a statement is accurate. Practicing with simple true or false questions can sharpen your ability to assess mathematical claims and enhance problem-solving skills.

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Most popular questions from this chapter

Let \(x=8, y=4,\) and \(z=2 .\) Write each phrase as an algebraic expression, and evaluate it. Assume that no denominators are \(0 .\) The quotient obtained when the product of \(x\) and \(y\) is divided by \(z\)

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