1.1 Choose The Correct Answer In Each Case. Write Only The Correspond With Correct Answer, E.g. 1.7 B Which Number Below Is Not A Natural Number? A. 2 B. 4 C. O D. 8 42 And 15?​

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Introduction

Natural numbers are a fundamental concept in mathematics, and they play a crucial role in various mathematical operations and theories. In this article, we will explore the concept of natural numbers, their properties, and how to identify them. We will also discuss some examples and exercises to help you understand the concept better.

What are Natural Numbers?

Natural numbers are positive integers that start from 1 and continue indefinitely. They are also known as counting numbers or positive integers. The set of natural numbers is denoted by the symbol N or ℤ+.

Properties of Natural Numbers

Natural numbers have several properties that make them unique and useful in mathematics. Some of the key properties of natural numbers include:

  • Closure: Natural numbers are closed under addition and multiplication. This means that when you add or multiply two natural numbers, the result is always a natural number.
  • Commutativity: Natural numbers are commutative under addition and multiplication. This means that the order of the numbers does not change the result.
  • Associativity: Natural numbers are associative under addition and multiplication. This means that the order in which you perform the operations does not change the result.
  • Existence of Identity: Natural numbers have an identity element for addition and multiplication. The identity element for addition is 0, and the identity element for multiplication is 1.

Examples of Natural Numbers

Here are some examples of natural numbers:

  • 1, 2, 3, 4, 5, ...
  • 10, 20, 30, 40, 50, ...
  • 100, 200, 300, 400, 500, ...

Exercises

Now that you have a good understanding of natural numbers, let's try some exercises to test your knowledge.

1.7 Which number below is not a Natural number?

A. 2 B. 4 C. 0 D. 8

Answer: C. 0

Explanation: Natural numbers are positive integers that start from 1 and continue indefinitely. Therefore, 0 is not a natural number.

1.8 Which of the following numbers is a Natural number?

A. 42 B. 15 C. 0 D. -5

Answer: A. 42

Explanation: Natural numbers are positive integers that start from 1 and continue indefinitely. Therefore, 42 is a natural number.

1.9 Which of the following numbers is not a Natural number?

A. 10 B. 20 C. 30 D. -5

Answer: D. -5

Explanation: Natural numbers are positive integers that start from 1 and continue indefinitely. Therefore, -5 is not a natural number.

Conclusion

In conclusion, natural numbers are a fundamental concept in mathematics that play a crucial role in various mathematical operations and theories. They have several properties that make them unique and useful, including closure, commutativity, associativity, and the existence of identity elements. By understanding natural numbers and their properties, you can better appreciate the beauty and complexity of mathematics.

References

Q: What are natural numbers?

A: Natural numbers are positive integers that start from 1 and continue indefinitely. They are also known as counting numbers or positive integers.

Q: What are some examples of natural numbers?

A: Some examples of natural numbers include:

  • 1, 2, 3, 4, 5, ...
  • 10, 20, 30, 40, 50, ...
  • 100, 200, 300, 400, 500, ...

Q: What are the properties of natural numbers?

A: Natural numbers have several properties that make them unique and useful in mathematics. Some of the key properties of natural numbers include:

  • Closure: Natural numbers are closed under addition and multiplication. This means that when you add or multiply two natural numbers, the result is always a natural number.
  • Commutativity: Natural numbers are commutative under addition and multiplication. This means that the order of the numbers does not change the result.
  • Associativity: Natural numbers are associative under addition and multiplication. This means that the order in which you perform the operations does not change the result.
  • Existence of Identity: Natural numbers have an identity element for addition and multiplication. The identity element for addition is 0, and the identity element for multiplication is 1.

Q: How do you identify a natural number?

A: To identify a natural number, you need to check if it is a positive integer. If it is, then it is a natural number.

Q: What is the difference between natural numbers and whole numbers?

A: Natural numbers are positive integers that start from 1 and continue indefinitely. Whole numbers, on the other hand, include 0 and all positive integers. Therefore, natural numbers are a subset of whole numbers.

Q: Can you give an example of a natural number that is not a whole number?

A: No, you cannot give an example of a natural number that is not a whole number. By definition, natural numbers are positive integers, and whole numbers include 0 and all positive integers. Therefore, all natural numbers are also whole numbers.

Q: Can you give an example of a whole number that is not a natural number?

A: Yes, an example of a whole number that is not a natural number is 0. While 0 is a whole number, it is not a natural number because natural numbers start from 1 and continue indefinitely.

Q: What is the importance of natural numbers in mathematics?

A: Natural numbers are a fundamental concept in mathematics, and they play a crucial role in various mathematical operations and theories. They are used to count and measure quantities, and they are the building blocks of more complex mathematical concepts.

Q: Can you give an example of a real-world application of natural numbers?

A: Yes, an example of a real-world application of natural numbers is in counting and measuring quantities in business and finance. For example, a company may use natural numbers to count the number of products it sells, or to measure the amount of money it earns.

Conclusion

In conclusion, natural numbers are a fundamental concept in mathematics that play a crucial role in various mathematical operations and theories. They have several properties that make them unique and useful, including closure, commutativity, associativity, and the existence of identity elements. By understanding natural numbers and their properties, you can better appreciate the beauty and complexity of mathematics.

References