- #1

RJLiberator

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## Homework Statement

Give an example of each, or state that the request is impossible:

1) A finite set that contains its infimum, but not its supremum.

2) A bounded subset of ℚ that contains its supremum, but not its infimum.

## Homework Equations

## The Attempt at a Solution

I either understand this perfectly, or am missing something with the definition of sup/inf not existing.

for 1) I have: Set B = { x ∈ ℚ : 1 < x < sqrt(2)} so inf(B) = 1 and sup(B) = DNE.

for 2) I have Set C = ( x ∈ ℚ : sqrt(2) < x < 2 } so inf(C) = DNE and sup(C) = 2.

At first, I thought by the axiom of completeness that question 1 would be impossible, but I seem to have found a set rather easily that is sufficient since I defined x to exist only in Q.