Open jonocarroll opened 10 months ago
The example of finding a function's fixed point using ⍣= confused me
⍣=
2÷⍨⍣=10 ⍝ Divide by 2 until we reach a fixed point
I understand that ⍣= will keep evaluating until the result no longer changes, but 10 (or any number) repeatedly divided by 2 only asymptotes to 0
10
2÷⍨⍣1⊢10 5 2÷⍨⍣2⊢10 2.5 2÷⍨⍣10⊢10 0.009765625 2÷⍨⍣100⊢10 7.888609052E¯30
so (I think) it only returns 0 because it loses precision.
0
I tried to find another more useful example. Application of the Collatz Conjecture always reaches 1, so that's perhaps not so interesting.
1
I suspect the canonical example of the Golden Ratio is more illuminating
+∘÷⍣1⍨1 2 +∘÷⍣2⍨1 1.5 +∘÷⍣3⍨1 1.666666667 +∘÷⍣=⍨1 1.618033989
Fair. Once 19.0 is out, I hope to do a wash up review. Thanks for taking the time.
The example of finding a function's fixed point using
⍣=
confused meI understand that
⍣=
will keep evaluating until the result no longer changes, but10
(or any number) repeatedly divided by 2 only asymptotes to 0so (I think) it only returns
0
because it loses precision.I tried to find another more useful example. Application of the Collatz Conjecture always reaches
1
, so that's perhaps not so interesting.I suspect the canonical example of the Golden Ratio is more illuminating