Alinear order is a binary operation that is antisymmetric,transitive, and total.
ID: 2938420 • Letter: A
Question
Alinear order is a binary operation that is antisymmetric,transitive, and total. A well-ordered relation is a linear orderwith the property that every non-empty subset S has a leastelement. Check if the sets - integers, rationals, and reals - arelinearly or well- ordered.I am stuck on what to docompletely. I have been just sitting and thinking how to do thisfor the last half hour and haven't come up withanything.
I am stuck on what to docompletely. I have been just sitting and thinking how to do thisfor the last half hour and haven't come up withanything.
Explanation / Answer
Hey, Q for you, do you happen to go to UCSB. But here you go, Remember, Antisymmetric is For all a,b A (aRb ^ bRa -->a=b) Transitive is for all a,b,c A (aRb ^ bRc ---> aRc) Total is sometimes called linear which is for all a,b A (aRbor bRa) (can be both!) Then if those 3 degrees check out, you have a linear order, andthen you check if it is well ordered if it has a least element(which if you have the test I think you do, you did in number2)
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