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Prove alpha=sup(S) is equivalent to alpha belongs to S closure 
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#1
Oct1210, 01:35 PM

P: 11

Given that alpha is an upper bound of a given set S of real numbers, prove that the following two conditions are equivalent:
a) We have alpha=sup(S) b) We have alpha belongs to S closure I'm trying to prove this using two steps. Step one being: assume a is true, then prove b is true. Step two being: assume b is true, then prove a is true. Could anyone help me with step two? Assuming alpha belongs to S closure..... 


#2
Oct1210, 02:01 PM

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P: 3,220

If I remember right, I think I gave you a useful condition for a point to be in the closure of a set. Do you see how you can use it here?



#3
Oct1210, 02:02 PM

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P: 3,220

Of course, your "steps" are a correct way to prove equivalence of statements, from a logical point of view.



#4
Oct1210, 06:03 PM

P: 11

Prove alpha=sup(S) is equivalent to alpha belongs to S closure
No I don't see how I can use it here in this problem.
How would I start my step two? I know I assume alpha belongs to S closure, but I am not sure where to go from there. 


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