In each part of this problem, display an example of a set M with the specific property or properties.
a) M does not equal R (R is the set of all real numbers), but M is bounded neither above nor below.
b) M is bounded above but fails to contain its least upper bound.
c) M is the set of integers that contains neither a smallest element nor a largest element.
d) M is not a set of integers but nevertheless contains both a smallest and a largest
Examples of sets that have specific properties are examined. The solution is detailed and well presented.