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#1 2011-04-17 14:59:43
- Kryptex_android
- Member
- Registered: 2011-04-17
- Posts: 5
equivalence relations using functions
Help me out with the question. I managed to do it myself somewhat, but would like a second opinion.
Let S be the set consisting of functions f : [0; 1] ! R such that
(i) f is continuous, and
(ii) f(x) > 0 for all x 2 [0; 1].
Show that the relation R on S defined by
fRg if and only if
∫1 and 0
f(x):dx ·
∫1 and 0
g(x):dx
is not a partial ordering on S.
Which out of reflexivity, antisymmetry, transitivity fails, and why?
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#2 2011-05-23 05:11:27
- JaneFairfax
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- Registered: 2007-02-23
- Posts: 6,868
Re: equivalence relations using functions
Do you mean
?
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