Least and greatest upper bound of a set

**mancillaj3** · February 16th 2009, 03:29 PM

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

**Reckoner** · February 16th 2009, 03:52 PM

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.

**mancillaj3** · February 16th 2009, 04:04 PM

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= $\lbrace<br />$ $\frac{4+x}{x}$ $\vert$ x
$\geq$
1 $\rbrace$

**Reckoner** · February 16th 2009, 04:09 PM

Originally Posted by mancillaj3

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= $\lbrace<br />$ $\frac{4+x}{x}$ $\vert$ x
$\geq$
1 $\rbrace$

For the last line, try

Code:

\text A=\left\{\left.\frac{4+x}x\;\right\vert\;x\geq1\right\}

which gives

$\text A=\left\{\left.\frac{4+x}x\;\right\vert\;x\geq1\ri ght\}$

**mr fantastic** · February 17th 2009, 03:47 AM

Originally Posted by mancillaj3

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= $\lbrace<br />$ $\frac{4+x}{x}$ $\vert$ x
$\geq$
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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