Where do they begin?

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

I thought it might begin in a CPU?

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.

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. I'm not precise. I've no idea of modern chip design. And yesterday I learnt the graphics card does counting these days. It is not that I lack precision. Or even there's woolly thinking. It's something more like I've a 80s mindset in a 20s world. Is that a good thing?

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.

Would a no deal Brexit lead to the field of small numbers, or through world trade be a return to the field of larger numbers for the UK? Musing...here.

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

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

....or own a chemistry set even.

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