Find infimum and supremum for the set A

[zxcvbs]

Hi, im trying to solve this problem for the defined sequence an. Find if exists supremum, infimum for the set A.

\(\displaystyle
\begin{array}{l}
Let{({a_n})_{n \in N}}\\
{a_n}: = 4 - \frac{9}{n}\\
A: = \{ {a_n}^2 - 3{a_n} - 10:n \in N\}
\end{array}
\)

I dont know how to start.

 

[stapel]

Hi, im trying to solve this problem for the defined sequence an. Find if exists supremum, infimum for the set A.

\(\displaystyle
\begin{array}{l}
Let{({a_n})_{n \in N}}\\
{a_n}: = 4 - \frac{9}{n}\\
A: = \{ {a_n}^2 - 3{a_n} - 10:n \in N\}
\end{array}
\)

I dont know how to start.

A good place to start might be with the definitions. What, exactly, are the "infimum" and "supremum" of a set?

Another place to start might be with the set's elements. What, exactly, are the elements of A? What are the first few terms of the sequence?

Please be complete. Thank you!