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Math Help - 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 \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

    \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 \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; February 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 \epsilon>0, find a number in the set that exceeds (l.u.b.A)- \epsilon and a number in the set that is smaller than (g.l.b. A)+ \epsilon.
    (a). A= \lbrace<br />
\frac{4+x}{x} \vertx
    \geq
    1 \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 \epsilon>0, find a number in the set that exceeds (l.u.b.A)- \epsilon and a number in the set that is smaller than (g.l.b. A)+ \epsilon.
    (a). A= \lbrace<br />
\frac{4+x}{x} \vertx
    \geq
    1 \rbrace
    For the last line, try
    Code:
    \text A=\left\{\left.\frac{4+x}x\;\right\vert\;x\geq1\right\}
    which gives

    \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 \epsilon>0, find a number in the set that exceeds (l.u.b.A)- \epsilon and a number in the set that is smaller than (g.l.b. A)+ \epsilon.
    (a). A= \lbrace<br />
\frac{4+x}{x} \vertx
    \geq
    1 \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 \epsilon>0, find a number in the set that exceeds (l.u.b.A)- \epsilon and a number in the set that is smaller than (g.l.b. A)+ \epsilon.

    \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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