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silvermane
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Prove the supremum exists :)
Let A = {x:x in Q, x^3 < 2}.
Prove that sup A exists. Guess the value of sup A.
First we show that it is non-empty. We see that there is an element, 1 in the set, thus A is non-empty.
Now we show that A is bounded. We see that 2 is not in the set, thus there must be an upper bound on our set. Our set can be represented as (-oo, 2).
Since A is bounded above, then supA exists, and we are done.
(I just need help clarifying and making sure that I am following the correct logic here.)
=)
Also, would supA = 2?
Thanks for all your help in advance
Homework Statement
Let A = {x:x in Q, x^3 < 2}.
Prove that sup A exists. Guess the value of sup A.
The Attempt at a Solution
First we show that it is non-empty. We see that there is an element, 1 in the set, thus A is non-empty.
Now we show that A is bounded. We see that 2 is not in the set, thus there must be an upper bound on our set. Our set can be represented as (-oo, 2).
Since A is bounded above, then supA exists, and we are done.
(I just need help clarifying and making sure that I am following the correct logic here.)
=)
Also, would supA = 2?
Thanks for all your help in advance