Start writing elements of each set. Plot them on a number line if you need to. How can you tell if you have a maximum or minimum element? How can you tell what the infimum or supremum of a set is? Use those definitions.
The question is:
For each of the following two sets, find the maximum, minimum, infimum, and supremum if they are definied. Justify your conclusions.
a. {1/n: n in N}
b. {x in R: x^2<2}
I don't even know where to begin. I think I am supposed to use the Archimedean Property...
Start writing elements of each set. Plot them on a number line if you need to. How can you tell if you have a maximum or minimum element? How can you tell what the infimum or supremum of a set is? Use those definitions.
If you really "don't even know where to begin" you probably should review the definitions of the words "maximum", "minimum", "supremum, and "infimum". In each of those problems, at least two of those should be fairly evident.