>>11538548Large numbers are a class of numbers.
Graham's number too, though even graham's number pales in comparison to Tree(3).
They're indeterminable. They're natural numbers with then same indeterminable properties as transcendental Real decimals like pi. They go on and on and on and on, and they're only proveably "finite" by the notion of transfinite arithmetic. That doesn't mean the exact number of digits are known, nor what those digits are. They make previously thought "infinite" decimals, like pi, seem completely rational. Pi has 50,000,000,000,000 digits discovered, and yet the amount of digits in TREE(3) couldn't even be shown if every digit was assigned a cubic planck length volume in the entire universe.
The fact that Large numbers exist in this capacity makes them indistinguishable from infinity. Calling them "Large" is somehow even disingenuous. They're arbitrarily large, indeterminable finite numbers.
"Arbitrarily large, indeterminably finite" is /exactly/ how cantor's set theory "guarantees" infinity to be, and by proxy exactly how computer math treats infinity.
Any ordered sequential set of naturals starting from 1->n contains the number that is used to describe it's size
[1,2,3] = size3, contains "3"
[1,2,3,4,5,6,7] = size7, contains "7"
= size?, contains "?"
aka Cantor, whether he realized it or not, inadvertantly allowed ? as a Natural finite number, but the only logical way that this could be true is if infinity is further described as being "an arbitrarily large, indeterminable finite number", such that you ought to never be able to reach it.
Cantor didn't know about Large numbers though. Almost all of them were products of the computer age, while cantor was alive between 1845-1918.
Basically, these "Large" numbers invalidate the fundamentals of set theory prescribed by Cantor. Not gonna say every idea in set theory is complete bullshit, but certainly sizes of ?.
