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ihatealgebrasomuch

  • 2 years ago

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

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  1. lstrasmann
    • 2 years ago
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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)

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

  3. TuringTest
    • 2 years ago
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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

  4. ihatealgebrasomuch
    • 2 years ago
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    so, .5 is a real number?

  5. TuringTest
    • 2 years ago
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    does it have any complex part in it ? an \(i\) or \(\sqrt1\) ?

  6. TuringTest
    • 2 years ago
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    I mean \(\sqrt{-1}\)

  7. estudier
    • 2 years ago
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    0.5 + 0i

  8. TuringTest
    • 2 years ago
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    oh you cheater :P

  9. estudier
    • 2 years ago
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    :-)

  10. TuringTest
    • 2 years ago
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    it must have a non-zero complex part to be exact

  11. TuringTest
    • 2 years ago
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    ...if it is *not* to be a real number, that is

  12. estudier
    • 2 years ago
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    But isn't the real line part of the complex plane?

  13. TuringTest
    • 2 years ago
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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 :/

  14. estudier
    • 2 years ago
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    s'K, just kidding a bit, it's the algebraist in me......

  15. TuringTest
    • 2 years ago
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    good habit ;)

  16. estudier
    • 2 years ago
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    I bet OP wish she never asked now.....:-)

  17. ihatealgebrasomuch
    • 2 years ago
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    so is .5 a real number???

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

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