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shahzadjalbani

  • 2 years ago

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

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

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

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

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

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

  6. nbouscal
    • 2 years ago
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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 \(\dfrac p q \)

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

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

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

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

  11. nbouscal
    • 2 years ago
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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.

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

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

  14. nbouscal
    • 2 years ago
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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.

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

  16. lgbasallote
    • 2 years ago
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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

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

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

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

  20. nbouscal
    • 2 years ago
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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.

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

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

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

  24. nbouscal
    • 2 years ago
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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 :)

  25. nbouscal
    • 2 years ago
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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

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

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

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

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