More than any other section in the book, I am having a hard time visualizing this (as much as Abstract Algebra can be visualized). In Theorem 6.8, are a, b, c, and d representing numbers? All of this new notation, including and especially "R/I", will take some getting used to.
If I understand this section accurately, then this is the method behind doing multiplication in my head. For example, if I={x in R 3y=x} and a=2, then 83=a+nx=2+(27)(3). Is this what they are saying?
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