I know what infimum and supremum are but I would like a bit of help with some notations "Find the infimum and supremum (if they exist) of:

1). $\displaystyle [1,3)$

2). $\displaystyle [1, \infty )$

3). $\displaystyle (-2,0) \cup (1,2)$

4). $\displaystyle \{1 - \frac{1}{n} : n \in \mathbb{N}\}$

5). $\displaystyle \{\frac{1}{2^{n}} - \frac{1}{3^{m}}: n, m \in \mathbb{N}\}$"

Now, this is where the notes we have begin and I don't know what it means when you have one [ bracket with a ) to close. So for the first one, is it just supremum = 3 and infimum = 1, or do the different brackets mean something special?

Here's my attempts:

1). 3, 1

2). none, 1

3). 2, -2

4). 1, 0

5). Should 0 be considered a natural number? I have not heard of a standard convention on this. Texts seem to go either way. This would change the result of this one and without knowing I don't know how to handle it.

* (As a side can anyone tell me the tex for the element of and natural, real, rational etc symbols?).