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shahzadjalbani Group Title

Please Explain the irrational numbers and rational numbers and differences between them and also explain irrational functions.

  • 2 years ago
  • 2 years ago

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  1. nbouscal Group Title
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    A number is rational if it can be written as the quotient of two integers.

    • 2 years ago
  2. nbouscal Group Title
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    This is why the set of rational numbers is denoted \(\mathbb Q\) for quotient.

    • 2 years ago
  3. shahzadjalbani Group Title
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    Please explain @nbouscal .

    • 2 years ago
  4. lgbasallote Group Title
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    other than the number itself over 1

    • 2 years ago
  5. lgbasallote Group Title
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    example...2 is rational because i can express it as 4/2

    • 2 years ago
  6. nbouscal Group Title
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    For any rational number there is a \(p\) and \(q\) with \(p,q\in\mathbb Z\) such that the rational number can be written as \(\dfrac p q \)

    • 2 years ago
  7. shahzadjalbani Group Title
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    Please mention differences between rational and irrational numbers also.

    • 2 years ago
  8. nbouscal Group Title
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    Irrational numbers are simply numbers that are not rational.

    • 2 years ago
  9. lgbasallote Group Title
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    pi cannot be expressed as a quotient even though 22/7 is near therefore it is irrational

    • 2 years ago
  10. shahzadjalbani Group Title
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    Some more examples ....@lgbasallote

    • 2 years ago
  11. nbouscal Group Title
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    The simplest proof of an irrational number is the one for \(\sqrt2\). http://www.homeschoolmath.net/teaching/proof_square_root_2_irrational.php shows the standard proof, due to the Greeks.

    • 2 years ago
  12. lgbasallote Group Title
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    ALL integers are rational numbers

    • 2 years ago
  13. lgbasallote Group Title
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    the integers are -1, -2, -3, 0, 1, 2, 3, etc

    • 2 years ago
  14. nbouscal Group Title
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    Decimal numbers that terminate are rational, because they can be written as a fraction. For example, 2.231 can just be written as 2231/1000. This is the case for any decimal that terminates.

    • 2 years ago
  15. shahzadjalbani Group Title
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    What about 1/3...................?@nbouscal @lgbasallote @ParthKohli

    • 2 years ago
  16. lgbasallote Group Title
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    some decimals that dont terminate can also be expressed as fractions...for example 0.333333 can be expressed as 1/3

    • 2 years ago
  17. nbouscal Group Title
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    1/3 is a quotient of two integers, so it is a rational number.

    • 2 years ago
  18. lgbasallote Group Title
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    that is rational because 1 amd 3 are integers

    • 2 years ago
  19. lgbasallote Group Title
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    do you get it now?

    • 2 years ago
  20. nbouscal Group Title
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    If you want to get even more fun you can look at the transcendental numbers, they are even more crazy than the irrational numbers. Irrational numbers that are not transcendental are called algebraic, they can be found as the roots of polynomials. There are all sorts of fun proofs to be read in this area of mathematics.

    • 2 years ago
  21. lgbasallote Group Title
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    lol why make it confusing :p

    • 2 years ago
  22. shahzadjalbani Group Title
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    Of coarse @lgbasallote is right.

    • 2 years ago
  23. lgbasallote Group Title
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    the kid doesnt understand rational and irrational and you're suggesting "fun" :p

    • 2 years ago
  24. nbouscal Group Title
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    Also worth noting is that the union of the rational and irrational numbers forms the real numbers, \(\mathbb R\), which is the set that you usually work in. You can also go further to \(\mathbb C\), the complex numbers. And then even further than that :)

    • 2 years ago
  25. nbouscal Group Title
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    I'm giving him an idea of the cool stuff ahead, it doesn't just stop at rational and irrational :P

    • 2 years ago
  26. lgbasallote Group Title
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    sometimes it's nicer to live in fantasies for some time

    • 2 years ago
  27. ParthKohli Group Title
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    1/3 has recurring digits but is still expressed as a quotient of two integers, so it is rational.

    • 2 years ago
  28. lgbasallote Group Title
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    i'd rather take the blue pill than the red

    • 2 years ago
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