Integer

Definition

An integer is a whole number, either positive, negative, or zero. Integers are fundamental mathematical concepts that play a crucial role in various areas of mathematics, including arithmetic, algebra, and number theory.

5 Must Know Facts For Your Next Test

1. Integers are used to represent quantities that cannot be divided, such as the number of people in a room or the number of days in a week.
2. Integers are essential in the context of subtracting integers, as the rules for subtracting positive and negative integers differ from the rules for subtracting positive numbers.
3. Integers can be raised to integer exponents, which is a fundamental operation in scientific notation and the study of exponential functions.
4. The set of integers, denoted by the symbol $\mathbb{Z}$, is one of the most important number systems in mathematics, along with the real numbers and the complex numbers.
5. Integers are closed under the operations of addition, subtraction, and multiplication, but not under division, as the result of dividing two integers may not be an integer.

Review Questions

• Explain how the concept of integers is relevant in the context of subtracting integers.
  • The concept of integers is crucial in the context of subtracting integers because the rules for subtracting positive and negative integers differ from the rules for subtracting positive numbers. When subtracting integers, the sign of the second number (the subtrahend) determines whether the operation is effectively an addition or a subtraction. For example, subtracting a positive integer is the same as adding the opposite (negative) integer, while subtracting a negative integer is the same as adding the positive integer. Understanding the properties of integers and how they interact with subtraction operations is essential for successfully solving problems involving the subtraction of integers.
• Describe the role of integers in the context of integer exponents and scientific notation.
  • Integers play a fundamental role in the context of integer exponents and scientific notation. Integer exponents, which can be positive, negative, or zero, are used to represent the power to which a base number is raised. This concept is crucial in scientific notation, a way of expressing very large or very small numbers using a combination of a decimal number and a power of 10. The exponent in scientific notation is always an integer, which determines the magnitude of the number. Understanding the properties of integers and how they interact with exponents is essential for manipulating and interpreting scientific notation effectively.
• Analyze the importance of the set of integers, denoted by $\mathbb{Z}$, in the broader context of mathematical number systems.
  • The set of integers, denoted by $\mathbb{Z}$, is one of the most fundamental and important number systems in mathematics. Integers, which include positive whole numbers, negative whole numbers, and zero, form the foundation for many mathematical concepts and operations. The set of integers is closed under the operations of addition, subtraction, and multiplication, making it a crucial building block for more advanced number systems, such as the real numbers and the complex numbers. Understanding the properties and relationships of integers within the broader context of mathematical number systems is essential for developing a strong foundation in mathematics and for solving a wide range of mathematical problems.

Related terms

Positive Integer: A positive integer is a whole number greater than zero, such as 1, 2, 3, and so on.

Negative Integer: A negative integer is a whole number less than zero, such as -1, -2, -3, and so on.

Zero: Zero is a unique integer that represents the absence of quantity or magnitude.