Find the maximum and minimum of each of the following subsets of R, if they exist justify the answer.
1) A = (0,3]
2) B = {x is a member of Z (integers): x < 1/2}
3) C = Q (Rationals) intersecting [-1, pi]
1) for the first question i would say that 3 is the maximum for the set since it is part of the set and therefore it is the supremum value and the notation says that the set is closed at this point, while at 0 this is left open and therefore a minimum does not exist.
2) For the second set since x is a member of integers and x < 1/2 the first element which satisfies this condition from the set of integers is 0 and hence 0 is a maximum value for the set based on the condition and the maximum exists, the minimum however doesnt exist and undefined as the minimum can take on any value be it -2,-3,-4..... etc.
3) the last question -1/1 can be expressed as a rational and hence since its a closed set -1 is a minimum value but in the case of a maximum value there exists an infinite amount of numbers that be as close to pi but the value itself and hence the maximum is not defined or rather undefined.
I was wondering based on my thinking if i have analysed the these problems correctly and i am hoping someone can just agree or deny my answers.