Results 1 to 11 of 11

Math Help - Proofs

  1. #1
    Junior Member
    Joined
    Jul 2006
    Posts
    73

    Proofs

    a) prove | |x| - |y| | <= | x - y |
    b) prove If | x-y | < c, then |x| < |y| + c
    c) prove If | x-y | < e for all e>0, then x = y
    d) X1....Xn are real numbers prove |X1 = X2 + ... + Xn| <= |X1| + |X2| + ..... + |Xn|
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,607
    Thanks
    1574
    Awards
    1
    #1
    |x|=|x-y+y|<=|x-y|+|y| -> |x|-|y|<=|x-y|
    Likewise |y-x|<=|y|-|x| -> |x|-|y|>= -|y-x|= -|x-y|
    Thus ||x|-|y||<=|x-y|.

    #3
    Suppose that x<>y. Then |x-y|>0 so let e=|x-y|.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jul 2006
    Posts
    73
    I follow problem one of what you did really well. I am confused on 3

    what is x<>y....does this just mean x = y, also why are you letting e = |x-y|, doesnt it say e is less than that....I know I am completely wrong because you have been right ever since you have started helping me. Maybe if you could explain it I would understand
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,607
    Thanks
    1574
    Awards
    1
    Well if x is not y then |x-y| is a positive number. Right?
    But for each positive number, e, |x-y|<e so |x-y|<|x-y|.
    But that is impossible! So x must be y.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Jul 2006
    Posts
    73
    ok, ic that makes alittle more sense that you explained it.
    I made a type on part D it should read this

    X1....Xn are real numbers prove |X1 + X2 + ... + Xn| <= |X1| + |X2| + ..... + |Xn|
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,607
    Thanks
    1574
    Awards
    1
    If you followed #1, then just apply the triangle inequality several times.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by luckyc1423 View Post
    b) prove If | x-y | < c, then |x| < |y| + c
    |x-y|<c

    |x-y|+|y|<c+|y|

    |x|=|x-y+y|<=|x-y|+|y|<c+|y|

    Thus,
    |x|<c+|y|
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Junior Member
    Joined
    Jul 2006
    Posts
    73
    Should these questions be easier for me to answer? I mean you guys come up with the solutions really quickly and I spend hours without even figure out how to do it. But I am at the average as far as grades for the course so I guess im not the only one struggling in the class.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by luckyc1423 View Post
    But I am at the average as far as grades for the course so I guess im not the only one struggling in the class.
    If it is your first time doing proofs, perhaps that is typical. It is also probably by far the most difficult class(es) out of all courses colleges offer.

    Why did you choose a math class instead of something else.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Junior Member
    Joined
    Jul 2006
    Posts
    73
    I am a math major, I have done extremely well in my other math classes and I have never gotten a C in any. Proofs just seem confusing to me for some reason.
    Follow Math Help Forum on Facebook and Google+

  11. #11
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by luckyc1423 View Post
    I am a math major, I have done extremely well in my other math classes and I have never gotten a C in any. Proofs just seem confusing to me for some reason.
    i feel your pain Lucky, its the same for me. making the leap from computational math to formal math is a big jump for people like us
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. proofs
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: March 2nd 2010, 03:54 AM
  2. lim sup and lim inf proofs
    Posted in the Differential Geometry Forum
    Replies: 6
    Last Post: February 24th 2010, 07:02 PM
  3. More Proofs
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: February 13th 2008, 07:05 PM
  4. Proofs
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 3rd 2008, 04:23 AM
  5. Replies: 3
    Last Post: October 6th 2007, 02:01 PM

Search Tags


/mathhelpforum @mathhelpforum