User blog comment:Wythagoras/Catching function in normal ordinals/@comment-11227630-20140203095754/@comment-5150073-20140625175913

The problem is that catching function isn't total if we define it in the recursive way. We're relying on "natural" FS's, but at some point, there might be different FS's which we can consider "natural", giving different values for C(a).