FizzBuzz in F# without if/else

let fb nn =

    // + and - operator are defined in Set.
    // operator for intersection of sets.
    let inline ( |^| ) a b = Set.intersect a b

    // an ideal of Z ring  (Z = field of integers)
    // http://en.wikipedia.org/wiki/Ideal_(ring_theory)
    let nZ n =
        seq { for i in 1 .. nn/n do yield i * n }
        |> Set.ofSeq

    // sets from ideals
    let all = nZ 1
    let z3 = nZ 3
    let z5 = nZ 5
    let z15 = z3 |^| z5   // (15) is m.c.m(3,5)

    // no buzz, no fizz...
    let onlynormal =
        all - (z3 + z5)
        |> Set.map (fun x -> (x, x.ToString()))

    // only "fizzes"
    let fizzes =
        z3 - z15 |> Set.map (fun x -> (x, "Fizz"))

    // only "buzzes"
    let buzzes =
        z5 - z15 |> Set.map (fun x -> (x, "Buzz"))

    // only "fizzbuzz"
    let buzzfizzes =
        Set.map ( fun x -> (x, "FizzBuzz")) z15

    // result
    // Note: apparently automatically sorts when convert the set to a list
    onlynormal + fizzes + buzzes + buzzfizzes
    |> Set.toList
    |> List.map (fun x -> snd x)

// -----------------------------------------------------------------------
// -- check ---
// first 102
printfn "1 - 102: %A" (fb 102)

// 597 position
printfn "597: %s" (fb 600).[597-1]

// 1200 position
printfn "1200: %s" (fb 1200).[1200-1]

// range
((fb 10000) |> List.toArray).[9900..9999] |> printfn "From 9901 to 10000: %A"

// WARNING: !!!!
// 49500 (over 1.000.000 elements!!!!!)
printfn "49500: %s" (fb 1000000).[49500-1]