For whatever reason I had the hardest time understanding why [1]={1,3,6} etc. Once I figured it out I felt really unintelligent. As well was the relation on page 179 for [a]. We had been talking about [a] before but for the second time we returned to the relation a=b. Having forgotten this I was confused as to why the relation that we had just talked about (x in Z such that x R a) was equal to x in Z such that x=a.
Something neat about equivalence classes was being able to predict the equality of [1] [3] and [6]. Since 1,3,6 were all related to each other, then [1]=[3]=[6]. The same went for the other integers as well. Also the use of the properties that we had just learned about was neat too. It provided for clever and elegant proofs, which are always enjoyable.
No comments:
Post a Comment