Mastering Real Numbers

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Questions and Answers

Which property of positive integers is discussed in Sections 1.2 and 1.3 of the text?

  • Fundamental Theorem of Arithmetic
  • Irrational numbers
  • Euclid's division algorithm (correct)
  • Long division process

What does the Euclid's division algorithm state?

  • Any positive integer can be divided by another positive integer in such a way that it leaves a remainder equal to the divisor.
  • Any positive integer can be divided by another positive integer in such a way that it leaves a remainder smaller than the divisor. (correct)
  • Any positive integer can be divided by another positive integer without leaving any remainder.
  • Any positive integer can be divided by another positive integer in such a way that it leaves a remainder greater than the divisor.

What is the main application of the Euclid's division algorithm discussed in the text?

  • Computing the LCM of two positive integers
  • Computing the HCF of two positive integers (correct)
  • Computing the remainder of two positive integers
  • Computing the sum of two positive integers

What is the other important property of positive integers discussed in the text?

<p>Fundamental Theorem of Arithmetic (D)</p> Signup and view all the answers

What does the Fundamental Theorem of Arithmetic state?

<p>Any positive integer can be expressed as a unique product of prime numbers. (A)</p> Signup and view all the answers

What is the main application of the Euclid's division algorithm?

<p>Computing the HCF of two positive integers</p> Signup and view all the answers

What are the two important properties of positive integers discussed in this chapter?

<p>Euclid's division algorithm and the Fundamental Theorem of Arithmetic</p> Signup and view all the answers

What is the other name given to irrational numbers?

<p>Real numbers</p> Signup and view all the answers

What is the name of the result that states any positive integer can be divided by another positive integer in such a way that it leaves a remainder smaller than the divisor?

<p>Euclid's division algorithm</p> Signup and view all the answers

What is the topic of discussion in this chapter?

<p>Real numbers</p> Signup and view all the answers

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