Understanding Irrational Numbers

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Questions and Answers

Which of the following is NOT a characteristic of irrational numbers?

  • They can be expressed as a ratio of two integers. (correct)
  • They are a contradiction of rational numbers.
  • They are usually represented as R\Q.
  • They cannot be expressed as simple fractions.

What does the symbol 'R\Q' represent regarding irrational numbers?

  • The set of rational numbers minus the set of real numbers.
  • The union of sets of real and rational numbers.
  • The set of real numbers minus the set of rational numbers. (correct)
  • The intersection of sets of real and rational numbers.

Which of the following is an example of an irrational number?

  • √4
  • √2 (correct)
  • -3/4
  • 1.5

What does the statement 'R – Q' imply about irrational numbers?

<p>Irrational numbers are a subset of real numbers but not rational numbers. (B)</p> Signup and view all the answers

How can irrational numbers be expressed?

<p>As a non-repeating and non-terminating decimal. (C)</p> Signup and view all the answers

Flashcards

Irrational Numbers

Real numbers that cannot be expressed as simple fractions or ratios.

Rational Numbers

Numbers that can be expressed as the ratio of two integers, where the denominator is not zero.

Set Representation of Irrationals

Irrational numbers are expressed as R\Q or R – Q.

Contradiction of Rational Numbers

Irrational numbers contradict the definition of rational numbers.

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Examples of Irrational Numbers

Numbers like π (pi) and √2 are famous examples of irrationals.

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Study Notes

Irrational Numbers

  • Irrational numbers are real numbers that cannot be written as a fraction of two integers.
  • They cannot be expressed as p/q, where p and q are integers, and q is not zero.
  • They are the opposite of rational numbers.
  • Irrational numbers are often shown as R\Q or R – Q.
  • R\Q represents the set of real numbers excluding the set of rational numbers.
  • R – Q represents the difference between a set of real numbers and a set of rational numbers.

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