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A comment on In Math You Have to Remember, In Other Subjects You Can Think About It. Parent comment

Re:In Math You Have to Remember, In Other Subjects You Can T... by yummyfajitas on Friday June 08, 2012 @09:11PM (#4086842)
No, it means you are starting with a different (but equivalent) set of axioms.

Our use of R rather than star-R is merely a quirk of history - we managed to justify R to ourselves first, hence it's the "standard".

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Re:In Math You Have to Remember, In Other Subjects You Can T... by podperson on Tuesday June 12, 2012 @02:11PM (#4101858)
You're working with strictly _more_ axioms, and the extra axioms don't seem justified unless you use the equivalence proof to show you haven't added undesired behavior.

(If you look at the other axioms, the hardest one to justify is the bounding axiom, and its necessity is reinforced by proof. Every other axiom fits in with the student's understanding of arithmetic.)

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