Additional Help with Order Isomorphisms

  • Thread starter PCSL
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In summary, the conversation is about someone looking for a resource similar to Paul's Online Notes for abstract algebra classes, specifically for set theory, functions, and isomorphisms of posets. They mention trouble with isomorphisms of posets and ask for recommendations for resources with proofs of related theorems. The other person suggests a site called proofwiki but notes that it may not have many proofs as it is a startup, and the person asking for help asks for any other recommendations for larger databases of proofs.
  • #1
PCSL
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I'm curious if there is a site like Paul's Online Notes for abstract algebra classes on set theory, functions, etc.

Lately I've been having trouble with isomorphisms of posets, so if there is a resource where I could view some proofs of theorems relating to isomorphisms of posets that would be awesome.

Thanks for any help you can offer, my textbook is fine - I'd just like some more practice.
 
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  • #2
I found a site called proofwiki but it did not have many proofs (seemed like it was a startup). Maybe you guys know of some larger databases of proofs?
 
  • #3
This will be the last time I'll bump this.
 

1. What is an order isomorphism?

An order isomorphism is a bijective function that preserves the ordering of elements between two partially ordered sets. In simpler terms, it is a mapping between two sets that maintains the same order of elements.

2. Why do we need additional help with order isomorphisms?

Additional help with order isomorphisms may be needed in order to understand more complex or abstract concepts, to apply them in specific contexts, or to solve more complicated problems that require a deeper understanding of order isomorphisms.

3. How do I identify if two sets are order isomorphic?

To identify if two sets are order isomorphic, you need to check if there exists a bijective function between them that preserves the ordering of elements. This means that for every element in one set, there is a corresponding element in the other set, and the relationships between the elements are maintained.

4. What are some real-life applications of order isomorphisms?

Order isomorphisms have various real-life applications, such as in computer science for data sorting and searching algorithms, in economics for comparing different currencies, and in social sciences for analyzing relationships between different variables.

5. Can order isomorphisms be used in infinite sets?

Yes, order isomorphisms can be used in infinite sets as long as they are partially ordered and there exists a bijective function between them that preserves the ordering of elements. However, it may be more challenging to identify and prove order isomorphisms in infinite sets compared to finite sets.

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