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I'm probably not very clever - but I don't get why calling the gap "fractions" is problematic. The example the author gives of "fractions" is... rational numbe
by awesome_dude 2y ago
I'm probably not very clever - but I don't get why calling the gap "fractions" is problematic.
The example the author gives of "fractions" is... rational numbers, and then proceeds to say "what about irrational numbers" - but in mymind (and this is probably where I'm a wrong?) an irrational number is still a fraction of a whole number, just we cannot express it "properly" (yet)
- bongodongobob 2y agoWell, you're wrong. An irrational number can't be described by a fraction. That's the very definition.
- cafeinux 2y agoThey mean "fraction" as in "part", the same way that an arm is a fraction of a whole body. But it's more about the words we use in everyday language than about mathematical definitions. Also, I think I remember that the definition of a rational number implies fractions of integers. Otherwise I could write π as π/1 and give you a rational representation of π.
- throwaway81523 2y ago"x is rational" means there are two integers p,q such that x=p/q. So for example, 2/3 is rational (p=2, q=3), but the square root of 2 is not rational (there is no such fraction). The last part is not very obvious (it greatly distressed the Pythagoreans when they figured it out) but there are a bunch of proofs in Wikipedia: https://en.wikipedia.org/wiki/Square_root_of_2#Proofs_of_irrationality https://en.wikipedia.org/wiki/Square_root_of_2#Proofs_of_irr...
- sadeshmukh 2y agoA fraction is some integer over another integer. Those are not fractions, though they may be in a colloquial sense.