Dan Drake 🦆6d ago

What would you say is the difference between "fraction" and "rational number"?

(Context: teaching an intro programming course and we have an example class for...these things. The existing materials call it "Fraction", but somehow I feel like RationalNumber or Rational would be better, but I can't articulate why.)

(Further context: I haven't looked up *anything* about this. Taking a "ask the hivemind first, do actual thinking later" approach...)

Show threadAleph ω+46d ago

@ddrake I would use the word "fraction" to denote a symbol consisting of two numerals and a fraction bar, whereas a rational number is the abstract thing that the fraction represents.

@mathematicalsynesthesia I think it'd be premature to say the rational numbers *are* the equivalence classes. At least, I don't think that's how most mathematicians think. (And we don't think of integers as equivalence classes of pairs of naturals either, and we don't think of naturals as finite transitive sets)

Show threadsoaproot
@aleph_omega_plus_four I was going to say something along those lines: that I'd say fraction if I am emphasizing the numerator and denominator, and rational number if that is not the focus. I might use them somewhat interchangeably, though. @ddrake @mathematicalsynesthesia
Mar 17 at 11:44pmWeb
Show threadsoaproot5d ago
@aleph_omega_plus_four @ddrake @mathematicalsynesthesia I'd probably restrict fraction to cases where the numerator and denominator are integers. Something like 0.5 / 3 or √2 / 2 I think I'd call a quotient (or maybe other terminology)