Ruby, fψ0(X(ΩM+X(ΩM+1ΩM+1)))+29(999) where M is the first Mahlo 'ordinal', X is the chi function (Mahlo collapsing function), and ψ is the ordinal collapsing function. f=->a,n,b=a,q=n{c,d,e=a;!c ?[q]:a==c ?a-1:e==0||e&&d==0?c:e ?[[c,d,f[e,n,b,q]],f[d,n,b,q],c]:n<1?9:!d ?[f[b,n-1],c]:c==0?n:[t=[...

This question already has a great answer, but I thought that you might like to see an actual piecewise construction of such a function (defined on $(-\ln(2),\infty)$). My function is not analytic, but it is continuous and differentiable on $\mathbb R$. First notice that if we find a function $h$...

Occasionally we have seen a situation like this: A user creates a new tag. The tag is then discussed on meta and the consensus is that the tag is not suitable and should be completely removed. However, it takes some time until somebody notices the tag and brings up the issue on meta. And then the...

What is the fastest growing total computable function you can describe in a few lines? Well, not necessarily the fastest - I just would like to know how far an ingenious mathematician can go using only a few lines, and what systematic approaches exist for this purpose. How farther you can go if ...

After having written quite a few programs related to large numbers and recursion over on ppcg.SE, I came up with this really interesting notation which I now call Simply's Ordinal Array Program (SOAP), and I'll explain a tweaked version that's nicer on the eyes than what my actual program does. ...

How can one prove the statement, "If a function grows fast enough, it cant be proven total in PA, unless PA is inconsistent"? How fast must it grow to be not provably total?