aufbahrung wrote:Where do they begin?

Flattering yourself again? This isn't a riff on mathematics. This is a riff on 'large' or on 'begin'. Stick with philosophy, where your shortcomings in precision will be less of a handicap for you.

If you're interested, there are books to read:

https://bookstore.ams.org/nml-6

But do consider this: the size of something depends in important ways on what it's being compared with. For a real treat, consult "relativism is self-refuting".

It's a poorly put question (since field is a word with a technical meaning in mathematics, which you clearly aren't using), but essentially a large number is an informal term for either a contextually large quantity (e.g. as the words appear in "the law of large numbers") or a number that is significantly bigger than those experienced in ordinary life (e.g. geological timescales or cosmic distances like those between galaxies).

It's not an area of mathematics, the question is purely a semantic one.

perhaps unsurprisingly there are loads of examples on wikipedia:
https://en.wikipedia.org/wiki/Large_numbers

Thommo wrote:It's a poorly put question (since field is a word with a technical meaning in mathematics, which you clearly aren't using), but essentially a large number is an informal term for either a contextually large quantity (e.g. as the words appear in "the law of large numbers") or a number that is significantly bigger than those experienced in ordinary life (e.g. geological timescales or cosmic distances like those between galaxies).

It's not an area of mathematics, the question is purely a semantic one.

perhaps unsurprisingly there are loads of examples on wikipedia:
https://en.wikipedia.org/wiki/Large_numbers

Yeah. Who could have guessed that there would be obvious places to make one's own start on such a question?

aufbahrung wrote:I thought it might begin in a CPU?

Not according to your OP, you didn't. And it doesn't begin with a CPU anyway, since people figured out how to do arbitrary-precision computation in software. You asked a lazy question.

I’ll see your CPU and raise you an abacus.
ETA CPUs have always been about speed of calculating, not size. That’s why we have exponents.

aufbahrung wrote:There's counting numbers. Field of large numbers begin when the counting numbers become uncountable.

Uncountable is also a term with a specific mathematical definition that you aren't using (relating to different sizes of infinity, also known as "cardinalities"). Consequently, in terms of mathematics this sentence is, I'm sorry to say, gibberish.

I can only surmise that what you're trying to say is that you think of large numbers as those which are beyond some arbitrary (you don't specify) level of computational complexity. If you want to think that, you can, I guess, since the term "large number" is no more technical or specific than the term "large man" or the term "large hill". I'm not sure there's anything to discuss in that, but maybe I'm misunderstanding something here.

aufbahrung wrote:There's counting numbers. Field of large numbers begin when the counting numbers become uncountable. This happens in the CPU since you can't count the numbers there albeit they are happening...

What is the name of the last countable number? (Hint: There is no such name.)

Which CPU does not "count the numbers there albeit they are happening"? Do you mean code that generates, say, the number 10^10^999 but there is insufficient resources, clock frequency and time to enumerate the list?

TREE(3) is infinitely closer to 1 than any "large number" along the "counting to infinity" line. So what?

On another hand,
Σp halts 2-|p| is uncomputable (Chaitin) but the number it calculates is less than 1.

Where do you want to go with this?

And this, children, is why you should always say no to drugs.

I was going to compose a few comments about finitism and computational feasibility, but meh. Doesn't seem worth it now.

Large enough?

My son thinks that 'hundred' is an unfeasibly large number which one uses to basically say 'a quantity beyond comprehension'. Is that what you're going for aufbahrung? Perhaps that number just gets larger with age then hits the final roof at zillions?