Question

Show that if a subset S has a maximum, then the maximum is also the supremum....

Show that if a subset S has a maximum, then the maximum is also the supremum. Similarly, show that if S has a minimum, then the minimum is also the infimum

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let F be an ordered field.  Let S be the subset [a,b) i.e, {x|a<=x<b, x element of...
Let F be an ordered field.  Let S be the subset [a,b) i.e, {x|a<=x<b, x element of F}. Prove that infimum and supremum exist or do not exist.
Let S be the set {(-1)^n +1 - (1/n): all n are natural numbers}. 1. find...
Let S be the set {(-1)^n +1 - (1/n): all n are natural numbers}. 1. find the infimum and the supremum of S, and prove that these are indeed the infimum and supremum. 2. find all the boundary points of the set S. Prove that each of these numbers is a boundary point. 3. Is the set S closed? Compact? give reasons. 4. Complete the sentence: Any nonempty compact set has a....
Show that a weakly open subset U of a Banach space is also open in the...
Show that a weakly open subset U of a Banach space is also open in the norm topology.
Let Y be a subspace of X and let S be a subset of Y. Show...
Let Y be a subspace of X and let S be a subset of Y. Show that the closure of S in Y coincides with the intersection between Y and the closure of S in X.
Show that for a subset S of R, bd(S) cannot contain an interval ((a,b),[a,b),(a,b],[a,b]).
Show that for a subset S of R, bd(S) cannot contain an interval ((a,b),[a,b),(a,b],[a,b]).
For any subset S ⊂ V show that span(S) is the smallest subspace of V containing...
For any subset S ⊂ V show that span(S) is the smallest subspace of V containing S. (Hint: This is asking you to prove several things. Look over the proof that U1+. . .+Um is the smallest subspace containing U1, . . . , Um.)
Consider the set S={0,2,4,6,8,10,12,14}.  Suppose you construct a subset of S by drawing elements randomly from S...
Consider the set S={0,2,4,6,8,10,12,14}.  Suppose you construct a subset of S by drawing elements randomly from S without replacement.   What is the minimum number of elements this subset must contain such that you can guarantee that at least one pair of elements in the subset sums to 18?
Prove : If S is an infinite set then it has a subset A which is...
Prove : If S is an infinite set then it has a subset A which is not equal to S, but such that A ∼ S.
show that each subset of R is not compact by describing an open cover for it...
show that each subset of R is not compact by describing an open cover for it that has no finite subcover . [1,3) , also explain a little bit of finite subcover, what does it mean like a finite.
In this problem, we will explore how the cardinality of a subset S ⊆ X relates...
In this problem, we will explore how the cardinality of a subset S ⊆ X relates to the cardinality of a finite set X. (i) Explain why |S| ≤ |X| for every subset S ⊆ X when |X| = 1. (ii) Assume we know that if S ⊆ hni, then |S| ≤ n. Explain why we can show that if T ⊆ hn+ 1i, then |T| ≤ n + 1. (iii) Explain why parts (i) and (ii) imply that for...