Understanding Closure Property: Sets of Numbers

This lesson explores the closure property in mathematics, focusing on various sets of numbers and operations. It explains how mathematicians group numbers into sets like natural numbers, whole numbers, integers, rational numbers, and irrational numbers. The lesson discusses the closure property under operations such as addition, subtraction, and division, highlighting which sets are closed under these operations. It emphasizes that closure involves a set of elements and an operation, and not all sets are closed under all operations.

Which set of numbers includes all the counting numbers plus zero?

• Integers

• Rational numbers

• Whole numbers

• Natural numbers

What is the result when you add two integers?

• A whole number

• Another integer

• An irrational number

• A rational number

Which set is closed under both addition and multiplication?

• Integers

• Irrational numbers

• Natural numbers

• Whole numbers

Why are whole numbers not closed under subtraction?

• Subtraction can result in a negative number

• Subtraction can result in a fraction

• Subtraction can result in an irrational number

• Subtraction can result in a decimal

Which set is closed under subtraction?

• Whole numbers

• Natural numbers

• Integers

• Irrational numbers

Why are whole numbers not closed under division?

• Division can result in a negative number

• Division can result in an irrational number

• Division can result in a fraction

• Division can result in a decimal

What is a limitation of closure with irrational numbers?

• Not all operations result in irrational numbers

• They are closed under multiplication

• They are closed under addition

• They are closed under subtraction