That's a rather narrow definition of comparability. If nothing else said, one would understand the term with regards to the relation of any partially ordered set – not only the one implicitly defined on that page.
I define a non-word "uncomparable" to mean something specific and rather arbitrary, but I do not intend it to be the antonym of the real word "comparable". I'll try to clarify this on the webpage you linked to. - Robert Munafo
I am certain it is greater. BB(n) grows super-exponentially.
In fact I would be willing to bet serious money that BB(n+1)/BB(n) is greater than BB(n) if 3 < n.
(This is, of course, assuming that one assumes that BB(n) is well-defined. That is an interesting point of philosophy given the existence of Turing machines which can't be proven to not halt.)
germanier|9 years ago
mrob27|9 years ago
scarmig|9 years ago
Is BB(26) - BB(25) greater than or less than BB(25)?
btilly|9 years ago
In fact I would be willing to bet serious money that BB(n+1)/BB(n) is greater than BB(n) if 3 < n.
(This is, of course, assuming that one assumes that BB(n) is well-defined. That is an interesting point of philosophy given the existence of Turing machines which can't be proven to not halt.)
strictnein|9 years ago