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Math Help - what proof to use

  1. #1
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    what proof to use

    I have a result and not sure what kind of proof to use to explain it.It's :

    let x be an integer, x^3 is even iff x is even


    thank you!
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  2. #2
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    iff means you have to do it both ways:

    x even => x^3 even
    x=2k
    x^3=2^3k^3
    x^3=2(4k^3)
    x^3=2m
    => even

    x^3 even => x even
    x^3=2k
    ...
    Hey you do the rest!

    -O
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  3. #3
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    Quote Originally Posted by nikie1o2 View Post
    let x be an integer, x^3 is even iff x is even
    HINT: (2k+1)^3 = 8k^3 +12k^2 +6k +1
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  4. #4
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    Quote Originally Posted by oswaldo View Post
    iff means you have to do it both ways:

    x even => x^3 even
    x=2k
    x^3=2^3k^3
    x^3=2(4k^3)
    x^3=2m
    => even

    x^3 even => x even
    x^3=2k
    ...
    Hey you do the rest!

    -O

    x^3=2^3k^3
    x^3=2(4k^3).......When you plugged in 2k how did you get those two steps?

    Would this be a direct proof?

    I hate proofs!!!
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  5. #5
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by nikie1o2 View Post
    x^3=2^3k^3
    x^3=2(4k^3).......When you plugged in 2k how did you get those two steps?
    x = 2k \implies x^3 = (2k)^3 = 2^3k^3 = 2 \cdot 2^2k^3 = 2(4k^3). if you are at the level where you are doing proofs like this, this is not a question you should be asking.

    Would this be a direct proof?
    yes it is

    for the second result, use the contrapositive. Plato gave you a hint for this
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  6. #6
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    Quote Originally Posted by nikie1o2 View Post
    I hate proofs!!!
    So why in the world do you torment yourself by taking mathematics courses?
    You do not have to take mathematics courses.
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  7. #7
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    I am passionate about math but proofs and logic are my weakness.
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  8. #8
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    Quote Originally Posted by nikie1o2 View Post
    I am passionate about math but proofs and logic are my weakness.
    Then you know nothing about mathematics!
    Mathematics is only about proofs.
    Numbers have almost nothing to do with mathematics.
    In fact, people who cannot do proofs cannot do mathematics.
    I fear that your passion is simply and tragically misplaced.
    So you must learn to do logic and proofs.
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  9. #9
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    nikie, math is definitely more than numbers. You can *count* on that. And try to improve yourself in proofs and logic. It ain't that hard.

    Hey Plato, I say Passion beats up any weakness.

    -O belives in 2nd chances.
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  10. #10
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    The question is answered, some harsh but valuable and well-intentioned advice has been given, and a debate about passion versus weakness is brewing.

    This thread has done it all and is now closed.

    The debate can continue in the Chat Room if so desired.
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