Actually that last point isn’t quite right, in the 1960s Robinson proved that the set of hyperreals were logically consistent if and only if the reals were.
This put to rest the age-long speculation that the hyperreals were questionable.
This speculation is a pain in the ass since it means that we primarily use limits when talking about this sort of thing.
Which is fine, but infinitesimals are the coolest shit ever
I did know about hyperreals, which is why I went with just “questionable”. IIRC you lose things like commutativity and associativity of arithmetic when you include extra numbers in the real line, and I feel like numbers should really have those.
Maybe that’s just my opinion though. Should I edit it?
Actually that last point isn’t quite right, in the 1960s Robinson proved that the set of hyperreals were logically consistent if and only if the reals were.
This put to rest the age-long speculation that the hyperreals were questionable.
This speculation is a pain in the ass since it means that we primarily use limits when talking about this sort of thing.
Which is fine, but infinitesimals are the coolest shit ever
I did know about hyperreals, which is why I went with just “questionable”.
IIRC you lose things like commutativity and associativity of arithmetic when you include extra numbers in the real line, and I feel like numbers should really have those.Maybe that’s just my opinion though. Should I edit it?Edit: I remembered very wrong. Fixing.