- #1
Skrew
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I was looking at the construction of the real number system.
I know dedekind cuts can be used(completely worthless in terms of understanding I think) and Cauchy sequences can be used (I wish my analysis book used them) but I would like to see a construction based on infinite decimal expansions.
I believe one exists as mentioned on wikipedia and my analysis book which does a really minimal job of it, but I can't find any information which goes into detail on how multiplication and division would be defined, etc.
Could you define it as a sequence of rational numbers in a decimal expansion and do something similar to the Cauchy sequence construction?
When ever I try to study analysis(self study, have not had a course yet) I always get bogged down into these details because I find them so interesting.
I know dedekind cuts can be used(completely worthless in terms of understanding I think) and Cauchy sequences can be used (I wish my analysis book used them) but I would like to see a construction based on infinite decimal expansions.
I believe one exists as mentioned on wikipedia and my analysis book which does a really minimal job of it, but I can't find any information which goes into detail on how multiplication and division would be defined, etc.
Could you define it as a sequence of rational numbers in a decimal expansion and do something similar to the Cauchy sequence construction?
When ever I try to study analysis(self study, have not had a course yet) I always get bogged down into these details because I find them so interesting.