Results 1 to 5 of 5

Math Help - Can someone explain why this line of reasoning concerning ordered relations is right?

  1. #1
    Newbie
    Joined
    Oct 2011
    Posts
    20

    Can someone explain why this line of reasoning concerning ordered relations is right?

    Choose δ ∈ (0,1) such that 1 - δ < x < 1 implies 3/M < 2x2 - 3x + 1 < 0; i.e., M/3 > 1/(2x2 - 3x + 1). Notice that 0 < x < 1 also implies 2 < x + 2 < 3. It follows that f(x) = (x+2)/(2x2 - 3x + 1) < M for all 1 - δ < x < 1.

    I do not understand the last statement because it seems to say that if 0 < a < b and d < c < 0, then ad < bc. Is this true?
    Last edited by lm1988; November 24th 2012 at 10:15 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,656
    Thanks
    1601
    Awards
    1

    Re: Can someone explain why this line of reasoning concerning ordered relations is ri

    Quote Originally Posted by lm1988 View Post
    Choose δ ∈ (0,1) such that 1 - δ < x < 1 implies 3/M < 2x2 - 3x + 1 < 0; i.e., M/3 > 1/(2x2 - 3x + 1). Notice that 0 < x < 1 also implies 2 < x + 2 < 3. It follows that f(x) = (x+2)/(2x2 - 3x + 1) < M for all 1 - δ < x < 1.
    I do not understand the last statement because it seems to say that if 0 < a < b and d < c < 0, then ad < bc. Is this true?

    Personally, I think that it is unreasonable for you to ask for explanation starting in the middle of someone's else proof.

    Why not simply state the actual question and ask for help?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2011
    Posts
    20

    Re: Can someone explain why this line of reasoning concerning ordered relations is ri

    Quote Originally Posted by Plato View Post
    Personally, I think that it is unreasonable for you to ask for explanation starting in the middle of someone's else proof.

    Why not simply state the actual question and ask for help?
    There is no question. I am just asking what the line of reasoning is as in the original post. The only additional information that you need to know is that M < 0 and is in R. This is actually how the proof begins.

    This is what I am trying to prove:
    Last edited by lm1988; November 24th 2012 at 11:04 AM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,656
    Thanks
    1601
    Awards
    1

    Re: Can someone explain why this line of reasoning concerning ordered relations is ri

    Quote Originally Posted by lm1988 View Post
    There is no question. I am just asking what the line of reasoning is as in the original post. The only additional information that you need to know is that M < 0 and is in R. This is actually how the proof begins.
    Again, without knowing the reason for that argument, it impossible to comment on the argument itself.

    Here is the best guess I have: if
    \begin{align*}\frac{3}{M} &< f <0\\ \frac{3}{fM} &> 1\\\frac{1}{fM} &>\frac{1}{3}\\ \frac{1}{f}&<\frac{M}{3}   \end{align*}.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Oct 2011
    Posts
    20

    Re: Can someone explain why this line of reasoning concerning ordered relations is ri

    Quote Originally Posted by Plato View Post
    Again, without knowing the reason for that argument, it impossible to comment on the argument itself.

    Here is the best guess I have: if
    \begin{align*}\frac{3}{M} &< f <0\\ \frac{3}{fM} &> 1\\\frac{1}{fM} &>\frac{1}{3}\\ \frac{1}{f}&<\frac{M}{3}   \end{align*}.
    The proof was provided in a textbook, so I am assuming that the author intended for the reader to understand the reason for that argument.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: September 19th 2011, 01:09 PM
  2. Relations, functions and ordered pairs.
    Posted in the Algebra Forum
    Replies: 11
    Last Post: April 29th 2010, 07:42 PM
  3. Replies: 4
    Last Post: December 15th 2009, 05:32 PM
  4. Ordered relations
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: September 21st 2009, 06:54 AM
  5. Totally Ordered Relations
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: October 13th 2007, 10:55 AM

Search Tags


/mathhelpforum @mathhelpforum