Merge pull request #4 from JuliaMath/teh/readme

Add content to the README

README.md

@@ -4,3 +4,62 @@ Interval Sets for Julia
 [![Build Status](https://travis-ci.org/JuliaMath/IntervalSets.jl.svg?branch=master)](https://travis-ci.org/JuliaMath/IntervalSets.jl)
 
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+
+This package represents intervals of an ordered set. For an interval
+spanning from `a` to `b`, all values `x` that lie between `a` and `b`
+are defined as being members of the interval.
+
+Currently this package defines one concrete type, `ClosedInterval`.
+These define the closed set spanning from `a` to `b`, meaning the
+interval is defined as the set `{x}` satisfying `a ≤ x ≤ b`. This is
+sometimes written `[a,b]` (mathematics syntax, not Julia syntax) or
+`a..b`.
+
+## Usage
+
+You can construct `ClosedInterval`s in a variety of ways:
+
+```julia
+julia> using IntervalSets
+
+julia> ClosedInterval{Float64}(1,3)
+1.0..3.0
+
+julia> 0.5..2.5
+0.5..2.5
+
+julia> 1.5±1
+0.5..2.5
+```
+
+The `±` operator may be typed as `\pm<TAB>` (using Julia's LaTeX
+syntax tab-completion).
+
+Intervals also support the expected set operations:
+
+```julia
+julia> 1.75 ∈ 1.5±1  # \in<TAB>; can also use `in`
+true
+
+julia> 0 ∈ 1.5±1
+false
+
+julia> intersect(1..5, 3..7)   # can also use `a ∩ b`, where the symbol is \cap<TAB>
+3..5
+
+julia> isempty(intersect(1..5, 10..11))
+true
+
+julia> (0.25..5) ∪ (3..7.4)    # \cup<TAB>; can also use union()
+0.25..7.4
+```
+
+When computing the union, the result must also be an interval:
+```julia
+julia> (0.25..5) ∪ (6..7.4)
+------ ArgumentError ------------------- Stacktrace (most recent call last)
+
+ [1] — union(::IntervalSets.ClosedInterval{Float64}, ::IntervalSets.ClosedInterval{Float64}) at closed.jl:34
+
+ArgumentError: Cannot construct union of disjoint sets.
+```