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shahzadjalbani

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

  • one year ago
  • one year ago

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

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

    • one year ago
  3. shahzadjalbani
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    Please explain @nbouscal .

    • one year ago
  4. lgbasallote
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    other than the number itself over 1

    • one year ago
  5. lgbasallote
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    example...2 is rational because i can express it as 4/2

    • one year ago
  6. nbouscal
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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 \(\dfrac p q \)

    • one year ago
  7. shahzadjalbani
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    Please mention differences between rational and irrational numbers also.

    • one year ago
  8. nbouscal
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    Irrational numbers are simply numbers that are not rational.

    • one year ago
  9. lgbasallote
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    pi cannot be expressed as a quotient even though 22/7 is near therefore it is irrational

    • one year ago
  10. shahzadjalbani
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    Some more examples ....@lgbasallote

    • one year ago
  11. nbouscal
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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.

    • one year ago
  12. lgbasallote
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    ALL integers are rational numbers

    • one year ago
  13. lgbasallote
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    the integers are -1, -2, -3, 0, 1, 2, 3, etc

    • one year ago
  14. nbouscal
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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.

    • one year ago
  15. shahzadjalbani
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    What about 1/3...................?@nbouscal @lgbasallote @ParthKohli

    • one year ago
  16. lgbasallote
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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

    • one year ago
  17. nbouscal
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    1/3 is a quotient of two integers, so it is a rational number.

    • one year ago
  18. lgbasallote
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    that is rational because 1 amd 3 are integers

    • one year ago
  19. lgbasallote
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    do you get it now?

    • one year ago
  20. nbouscal
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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.

    • one year ago
  21. lgbasallote
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    lol why make it confusing :p

    • one year ago
  22. shahzadjalbani
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    Of coarse @lgbasallote is right.

    • one year ago
  23. lgbasallote
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    the kid doesnt understand rational and irrational and you're suggesting "fun" :p

    • one year ago
  24. nbouscal
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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 :)

    • one year ago
  25. nbouscal
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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

    • one year ago
  26. lgbasallote
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    sometimes it's nicer to live in fantasies for some time

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

    • one year ago
  28. lgbasallote
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    i'd rather take the blue pill than the red

    • one year ago
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