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ihatealgebrasomuch Group Title

what exactly is a 'real number' does that mean whole # or can it be like .5?

  • one year ago
  • one year ago

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  1. lstrasmann Group Title
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    yeah, i think real numbers can be basically any number on the number line (including decimals and fractions) according to wikipedia it includes integers fractions and unrational numbers (Pi for example)

    • one year ago
  2. estudier Group Title
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    whole # - this is not defined by mathematicians (use integer, positive integer, natural number, etc)

    • one year ago
  3. TuringTest Group Title
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    a real number is any number that appears on the real line; i.e. does not have an imaginary (complex) part complex numbers involve \[i=\sqrt{-1}\]which is not a real number, because there is no real number \((-\infty,\infty)\) number that satisfies \(\sqrt{-1}\) our guesses might be 1 and -1, but...\[1\cdot1=1\neq-1\]and\[(-1)(-1)=1\neq-1\]so there is no "real" number that satisfies the expression real numbers in no way have to be whole numbers

    • one year ago
  4. ihatealgebrasomuch Group Title
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    so, .5 is a real number?

    • one year ago
  5. TuringTest Group Title
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    does it have any complex part in it ? an \(i\) or \(\sqrt1\) ?

    • one year ago
  6. TuringTest Group Title
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    I mean \(\sqrt{-1}\)

    • one year ago
  7. estudier Group Title
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    0.5 + 0i

    • one year ago
  8. TuringTest Group Title
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    oh you cheater :P

    • one year ago
  9. estudier Group Title
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    :-)

    • one year ago
  10. TuringTest Group Title
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    it must have a non-zero complex part to be exact

    • one year ago
  11. TuringTest Group Title
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    ...if it is *not* to be a real number, that is

    • one year ago
  12. estudier Group Title
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    But isn't the real line part of the complex plane?

    • one year ago
  13. TuringTest Group Title
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    all real numbers are complex, not all complex are real if I am phrasing it poorly above I am only being too lazy since I'm about to leave, sorry :/

    • one year ago
  14. estudier Group Title
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    s'K, just kidding a bit, it's the algebraist in me......

    • one year ago
  15. TuringTest Group Title
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    good habit ;)

    • one year ago
  16. estudier Group Title
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    I bet OP wish she never asked now.....:-)

    • one year ago
  17. ihatealgebrasomuch Group Title
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    so is .5 a real number???

    • one year ago
  18. estudier Group Title
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    A simple answer is that pretty much all the numbers you are used to (including 0.5) are real.

    • one year ago
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