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m00npirate
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I've been looking around for this, but I can't find any discussion of non-integer moduli for use in modular arithmetic. Is it not defined simply because it isn't useful? Every source I look at will say "integers a and b are congruent modulo n if blah blah blah." However, it makes just as much sense to say [itex] \pi + \sqrt{2} \equiv \sqrt{2} \hspace{7 mm}(mod \pi)[/itex].
<strike> The reason I'm wondering about this is because every circle would have zero circumference and area [itex](mod \pi)[/itex] which seemed absurd. Can anyone explain? </strike>Thanks a ton!
EDIT: Just realized I was being silly, as obviously most circles will still be fine .But is there a physical way to interpret this for those circles with 0 circumference but non-zero area etc? Or is modular arithmetic just not useful here?
<strike> The reason I'm wondering about this is because every circle would have zero circumference and area [itex](mod \pi)[/itex] which seemed absurd. Can anyone explain? </strike>Thanks a ton!
EDIT: Just realized I was being silly, as obviously most circles will still be fine .But is there a physical way to interpret this for those circles with 0 circumference but non-zero area etc? Or is modular arithmetic just not useful here?
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