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Thread: Least and greatest upper bound of a set

  1. #1
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    Least and greatest upper bound of a set

    please help, i dont know how to post on latex, for example the attachment is on the link below but I dont know how to post on this message
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    Just surround your $\displaystyle \text\LaTeX$ code with [tex] and [/tex]. The board sets math mode automatically, so don't use dollar signs around everything.

    For example:

    Code:
    [tex]\sum_{n=1}^\infty\frac1n=\frac{\pi^2}6[/tex]
    Produces

    $\displaystyle \sum_{n=1}^\infty\frac1{n^2}=\frac{\pi^2}6$

    Use \text{} to get regular non-math text. There are limits on the number of characters and the size of each $\displaystyle \text\LaTeX$ image, so you may need to break things up into several sections. For full paragraphs of text, like in your PDF, post the non-math text outside of the [tex] tags.
    Last edited by Krizalid; Feb 17th 2009 at 06:50 AM.
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    Find the least upper bound and the greatest lower bound of the following sets. For a given $\displaystyle \epsilon$>0, find a number in the set that exceeds (l.u.b.A)-$\displaystyle \epsilon$ and a number in the set that is smaller than (g.l.b. A)+ $\displaystyle \epsilon$.
    (a). A=$\displaystyle \lbrace
    $$\displaystyle \frac{4+x}{x}$$\displaystyle \vert$x
    $\displaystyle \geq$
    1$\displaystyle \rbrace$
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    Quote Originally Posted by mancillaj3 View Post
    Find the least upper bound and the greatest lower bound of the following sets. For a given $\displaystyle \epsilon$>0, find a number in the set that exceeds (l.u.b.A)-$\displaystyle \epsilon$ and a number in the set that is smaller than (g.l.b. A)+ $\displaystyle \epsilon$.
    (a). A=$\displaystyle \lbrace
    $$\displaystyle \frac{4+x}{x}$$\displaystyle \vert$x
    $\displaystyle \geq$
    1$\displaystyle \rbrace$
    For the last line, try
    Code:
    \text A=\left\{\left.\frac{4+x}x\;\right\vert\;x\geq1\right\}
    which gives

    $\displaystyle \text A=\left\{\left.\frac{4+x}x\;\right\vert\;x\geq1\ri ght\}$
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  5. #5
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    Quote Originally Posted by mancillaj3 View Post
    Find the least upper bound and the greatest lower bound of the following sets. For a given $\displaystyle \epsilon$>0, find a number in the set that exceeds (l.u.b.A)-$\displaystyle \epsilon$ and a number in the set that is smaller than (g.l.b. A)+ $\displaystyle \epsilon$.
    (a). A=$\displaystyle \lbrace
    $$\displaystyle \frac{4+x}{x}$$\displaystyle \vert$x
    $\displaystyle \geq$
    1$\displaystyle \rbrace$
    So, for the record, the actual question that the OP wants an answer for is:

    Find the least upper bound and the greatest lower bound of the following sets. For a given $\displaystyle \epsilon$>0, find a number in the set that exceeds (l.u.b.A)-$\displaystyle \epsilon$ and a number in the set that is smaller than (g.l.b. A)+ $\displaystyle \epsilon$.

    $\displaystyle \text A=\left\{\left.\frac{4+x}x\;\right\vert\;x\geq1\ri ght\}$
    l.u.b. = 5, g.l.b. = 1. Do you see why?
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