`RealInfinity` is abstract, but the package assumes it has exactly two subtypes

RealInfinity is declared abstract and exported, which invites downstream subtypes:

abstract type RealInfinity <: Real end
struct PositiveInfinity <: RealInfinity end
struct NegativeInfinity <: RealInfinity end

However signbit is defined only on the two concrete types, with no ::RealInfinity fallback, and sign, angle and every T(x::RealInfinity) conversion are built on it:

signbit(::PositiveInfinity) = false         # src/Infinities.jl:52-53
signbit(::NegativeInfinity) = true
sign(y::RealInfinity) = 1-2signbit(y)       # :71
angle(x::RealInfinity) = π*signbit(x)       # :72
_convert(::Type{T}, x::RealInfinity) where {T<:Real} = sign(x)*convert(T, Inf)   # :64

So a third subtype does not fail cleanly:

julia> struct ThirdInfinity <: Infinities.RealInfinity end

julia> signbit(ThirdInfinity())
ERROR: StackOverflowError:

julia> Float64(ThirdInfinity())
ERROR: StackOverflowError:

It falls through to Base.signbit(x::Real) = x < 0 (number.jl:137) and the comparison then recurses.

Two ways to make the assumption explicit:

1. Non-breaking — add a signbit(::RealInfinity) fallback that throws a clear error, so an unsupported subtype produces a message instead of a stack overflow.

2. Breaking — put the closure in the type system:

   struct PositiveInfinity <: Real end
   struct NegativeInfinity <: Real end
   const RealInfinity = Union{PositiveInfinity, NegativeInfinity}
   

The second option is what was probably intended, at least if the intent is that the extended real line has exactly two points at infinity — with directional infinities living in ComplexInfinity{T} — then option 2 states that in the type system rather than in convention.

Start in src/Infinities.jl at the signbit methods and RealInfinity-dependent sign, angle, and conversion definitions. Reproduce the ThirdInfinity examples to confirm the recursive failure, then determine whether the project intends a rejecting fallback or a closed type representation. Done means unsupported subtypes fail clearly or the two-infinity constraint is enforced, with regression coverage for the reported behavior.