# Thread: Least and greatest upper bound of a set

1. ## 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

2. Just surround your $\displaystyle \text\LaTeX$ code with $$and$$. The board sets math mode automatically, so don't use dollar signs around everything.

For example:

Code:
$$\sum_{n=1}^\infty\frac1n=\frac{\pi^2}6$$
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.

3. 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$\displaystyle \rbrace$

4. Originally Posted by mancillaj3
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

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

5. Originally Posted by mancillaj3
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?