I've heard that 2 to the power of 2, to the power of 2, etc... 6 times is a number so huge that we could never figure it out. Would that qualify as being infinite? And how would we be able to intelligibly come to that conclusion, or is it a "rough estimate" that we could never figure it out?
Thank you for your time.
If I understand well the number you have in mind, 2^2^2^2^2^2, it is not all that large: 2 2^2 = 4 4^2 = 16 16^2=256 256^2=65,536 65,536^2=4,294,967,296 The person you heard this from may have had another number in mind, namely: 2^(2^(2^(2^(2^2)))). Let's construct this one: 2 2^2 = 4 2^4 = 16 2^16 = 65,536 2^65,536 = ??? .... and this fifth step (bringing in the fifth "2") already goes beyond most ordinary spreadsheets and calculators. Still, since 2^10 is about 10^3, we can estimate the result to be around 10^19661, i.e. a "1" with nearly 20,000 zeros. A good computer could probably do the calculation and could print out the resulting number on perhaps 12 pages or so. The sixth step, taking 2 to the power of this number, would really go beyond what most of us can even imagine. It would bring us to a number -- let's call it "K" in your honor -- that, written in the decimal notation, would have so many digits that this number of...