It is possible to create Rationals with 0 denominator

[KristofferC]

julia> 1//0
1//0

julia> div(1,0)
ERROR: DivideError: integer division error
Stacktrace:
 [1] div(::Int64, ::Int64) at ./int.jl:144

Should 1//0 also error out?

[yuyichao]

I believe this is intentially used to represent infinity

julia> typemax(Rational{Int})
1//0

[JeffBezanson]

Yes, this was intentional.

julia> convert(Rational, Inf)
1//0

[bramtayl]

The left and right hand limits disagree: -Inf and +Inf respectively.

[yuyichao]

The left and right hand limits disagree: -Inf and +Inf respectively.

You mean -Inf != Inf and -1//0 != 1//0?

[bramtayl]

No 1//a really small positive number is a large positive number, but 1//a really small negative number is a large negative number

[yuyichao]

This is not at all aiming for a solution that's mathematically rigorous or even correct so what's the limit of 1/a in math at 0 does not matter at all. Also note that there isn't a equivalent // in math and 1//a in julia does not accept floating point number so it doesn't even make sense to talk about the limit here.

This is also exactly the same behavior as floating point division 1 / 0 vs -1 / 0.

[StefanKarpinski]

Since 1 is the smallest non-zero integer value you can divide by, this is a non-issue. It also doesn't really matter how we choose to represent ±inf as rationals as long as they behave correctly.