Abstract: If we begin with a notion of number N that we denote F(N) as a function of time, can a decidable procedure exist on definability of the hierarchical growth of numbers? Inspired by Tipler's Omega point and Thomson's lamp, what would be the limiting behavior of a function F(N) as it becom...
Perhaps I should add the physics-tag; my motivation was Poincare recurrence theorem, or rather what happens when the number exceeds all the particles in the universe.
@StephanSchielke What happens if the number of 0s exceed the number of particles in the universe? Also, the last statement then rests upon faith as opposed to logic akin to saying "I can't imagine God, but I know He exists." When does the notion of Existence cease to have existence..or meaning?
Closing for the time pending some specification of the problem. This is really broad and vague -- and more than a little confusing. What sort of answer might you be expecting? As @AlexBecker is asking: what specific issue might you be trying to solve here? What exactly would you like someone from the community to explain to you?
My initial question was the one in thought experiment re: "understanding and philosophy of the number system" when a number grows fast. I do believe I have received partial answer from various answerer. It's unfair that it got closed and I do not have sufficient privelege to vote to reopen.
Keep in mind closure isn't (doesn't have to be) permanent; I would encourage you to develop your question a bit further to more clearly indicate precisely what you'd like someone from the community to explain to you. I'd be delighted to reopen after an appropriate revision responding to the requests for clarification
Discussion between Mahmud and Joseph …
Discussion between Mahmud and Joseph …