fix definition of Z, R, N and Q (#94)

[daanhb]

94

[codecov[bot]]

Codecov Report

Merging #95 (26e5a16) into master (6b7983d) will increase coverage by 0.14%. The diff coverage is 96.66%.

@@            Coverage Diff             @@
##           master      #95      +/-   ##
==========================================
+ Coverage   84.79%   84.94%   +0.14%     
==========================================
  Files          30       31       +1     
  Lines        2387     2417      +30     
==========================================
+ Hits         2024     2053      +29     
- Misses        363      364       +1     

Impacted Files	Coverage Δ
src/DomainSets.jl	100.00% <ø> (ø)
src/generic/canonical.jl	69.76% <ø> (ø)
src/generic/domain.jl	91.80% <ø> (ø)
src/domains/numbers.jl	93.75% <93.75%> (ø)
src/domains/trivial.jl	94.36% <100.00%> (+1.38%)	:arrow_up:

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[dlfivefifty]

Why remove them when implementing is very straightforward?

[daanhb]

Did you have an implementation in mind? I was thinking we could make a strict "StrictFullSpace{T}" (or something with a better name) which contains x if x is of type T, or if convert(T, x) works. That might be useful elsewhere too.

[daanhb]

It's like a TypeDomain, the domain of all instances of a certain type

[dlfivefifty]

Why not:

struct Integers end
in(x, ::Integers) = isinteger(x)

[daanhb]

I've done both, more strict full spaces called TypeDomain and specific number sets like Integers. The isinteger function seems indeed most appropriate to define the set of integers. The isreal function allows real arrays (intentionally), so I had to exclude those for the set of real numbers. It's a pity there are no generic functions isnumber, iscomplex and isrational.

Anyway:

julia> π ∈ ℤ
false