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Library for validated numerics using interval arithmetic

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Is there anything to stop us using `Interval(NaN, NaN)` as the representation of the empty interval? I think this would remove the need for a lot of `isempty` checks, and...

The rational number `1//10` does not have an exact floating point representation. However currently ```julia julia> x = Interval{Float64}(1//10) [0.1, 0.100001] julia> x.lo == x.hi true ``` So the interval...

Currently `Plots.jl` ignores objects that extend to infinity. When plotting we should check for an infinity and replace it by a large finite number of the same sign.

Currently, we are getting ``` julia> @interval("[1.0000000000000001, 1.0000000000000002]") Interval(1.0, 1.0) ``` Expected Answer ``` Interval(1.0, 1.0000000000000002) ``` This is because of ``` julia> rationalize(1.0000000000000002) 1//1 ``` It should not be...

Currently we have ``` julia> DecoratedInterval(1..2, com) == DecoratedInterval(1..2, trv) true ``` Is this specified in the standard? cc @krish8484

All the changing or rounding of values must be done by `@interval` and `I"..."`.

```jl julia> X = 3..4 [3, 4] julia> @which X / 3.1 /(a::Interval{T}, x::T) where T @which X / Float32(3.1) /(x::Number, y::Number) in Base at promotion.jl:314 ``` The version with...

```jl IntervalBox{Float32}(X::IntervalBox) = IntervalBox(Interval{Float32}.(X)) ```

Intervals using `..` cannot be parsed properly from strings. ```julia julia> I"1..2" [1, 1] julia> @interval "1..2" [1, 1] @biginterval "1..2" [1, 1]₂₅₆ ``` Obtained using Julia 1.4.0, IntervalArithmetic v0.17.3