Curry
  • Curry
Help with equivalence relations and partial orders.
Mathematics
katieb
  • katieb
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Curry
  • Curry
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Curry
  • Curry
I can think of many examples for the other way around, but not for that... :/
zzr0ck3r
  • zzr0ck3r
What is the two definitions?

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Curry
  • Curry
Well for partial order, you need anti-symmetry. For equivalence you just need symmetry. But both need reflexive and transitive.
zzr0ck3r
  • zzr0ck3r
hint: think subsets
zzr0ck3r
  • zzr0ck3r
does \(A\subset B \) imply \( B \subset A\)?
Curry
  • Curry
Not unless they are equal.
zzr0ck3r
  • zzr0ck3r
ps I made another comment on your last post
zzr0ck3r
  • zzr0ck3r
correct
Curry
  • Curry
oh kk, i'll go look at it! thakn you!
zzr0ck3r
  • zzr0ck3r
so subset inclusion is a partial order and not a equivalence relation
Curry
  • Curry
OO, that makes sense! and when it says define the universal set, what does that mean?
zzr0ck3r
  • zzr0ck3r
just pick a set like \(\mathbb{N}\)
zzr0ck3r
  • zzr0ck3r
so the universal set would be \(P(\mathbb{N})\) (The set of all subsets of \(\mathbb{N}\))
Curry
  • Curry
ooo! gotchya gotchya thanks!
zzr0ck3r
  • zzr0ck3r
np

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