I know that it's simple enough to map the integers, $\mathbb{Z}$, to pairs of integers, $\mathbb{Z}^2$, in a bijective way (i.e. a one-to-one mapping). You can wrap the integers around the origin of the 2D Cartesian grid like a spiral, or you can use some space filling curve, or you can map the i...
@ASCII-only I don't know, I doubt you could always find a direct "mathematical equivalent". I mean many very mathematical things are not very explicit.
Ruby, 348 bytes, fψ0(ψ9(9))(9)
where f is the fast growing hierarchy and ψ is an ordinal collapsing function described below.
Try it online!
def f(b,n=0,x=0)c,d=b;n<1?(b.class!=Array):x>0?(n.times{n+=b==1?n:f(f(b,n),n,1)};n):f(b)?(b>1?b-1:n):b.size>2?h(n,c,d):f(d)?(d>1?[c,d-1]:d>0?c:[c,n]):[c,...
Does anyone think my explanation is too advanced/complicated and that I need to dumb it down?
I am not a mathematician but I am interested in big numbers. I find them to be really interesting, almost god-like.
I am watching a series of videos from David Metzler on youTube. I have a basic understanding of some fast growing functions. David does not cover Tree(n) which I've read is one ...
about the fgh aproximation of TREE(3)? I guess I mainly need a refresher on what the phi function does exactly, it was something with defining ordinals as the n-th fixed point of the previous ordinal set
@SimplyBeautifulArt I'm still at the start of the messages you linked me too but for me it seems to help to imagen a succesor function S(a) = lambda x:a so ω+1 is just {ω,ω,ω,...} to me
I'm vaguely familar with the hardy hierachy but it seems pretty simple to me H(0,n)=n H(a,n)=H(a(n),n) (if you use that successor thing you don't even need to handle integers separately)
@SimplyBeautifulArt so why did you go way past the Bachmann-Howard ordinal in your answer? Isn't the Bachmann-Howard ordinal much much huger than the Small Veblen Ordinal? (after this I will let you explain to wizzwizz4 (or even try to help if I can))
I don't think I can talk at the moment. Perhaps in ~10 hours my connection will be back. I'm having a storm right now and my phone line is probably down half the time.
Ruby, 348 bytes, fψ0(ψ9(9))(9)
where f is the fast growing hierarchy and ψ is an ordinal collapsing function described below.
Try it online!
def f(b,n=0,x=0)c,d=b;n<1?(b.class!=Array):x>0?(n.times{n+=b==1?n:f(f(b,n),n,1)};n):f(b)?(b>1?b-1:n):b.size>2?h(n,c,d):f(d)?(d>1?[c,d-1]:d>0?c:[c,n]):[c,...
I am not a mathematician but I am interested in big numbers. I find them to be really interesting, almost god-like.
I am watching a series of videos from David Metzler on youTube. I have a basic understanding of some fast growing functions. David does not cover Tree(n) which I've read is one ...
