If you make inferences that are truth-preserving, precise, and consistent you're doing mathematics. Brent Meeker On 7/6/2015 11:09 AM, Dan Asimov wrote:
There are several different mathematicses that would each have its own definition, including at least the following:
1) The human culture of any field that uses mathematics to study something
2) The human culture of mathematicians studying pure math (the study of deriving rigorous results from rigorous rules*)
3) The study of deriving rigorous results from rigorous rules per se
4) The body of past, present, future rigorous results from rigorous rules
5) The body of past, present, future rigorous results from axiom schema of any cardinality
This last one besides being interesting in its own right includes, e.g., all exactly definition of the integers, satisfying Platonists of all stripes
—Dan
____________________________________________________________________ * "Here "rigorous rules" meaning a finite collection of axiom schema _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun