Talk:Large numbers

OK, this is a first stab at getting all the large number topics together, please feel free to kick this into shape. The Anome

Can I suggest that we include only pure numbers in this article, not distances and other measurements? Would anyone object if I deleted the astronomical distances, since they are only large numbers when expressed in small units? I suppose I should go further and say that Avogradro's number is also just an arbitrary unit, but I shan't, because I feel I'm on a slippery slope towards excluding everything! -- Heron

Then why do people call large numbers "astronomical", as the article informs us? Perhaps it's because astronomical distances are large when expressed in any human-sized scale. I think the concept of "largeness" needs to be explained. The whole article is subjective anyway -- I wouldn't call 10¹⁰ large, I deal with those sorts of numbers every day. <math>10^{10^{10}}<math> is more like it. -- Tim Starling 09:26 18 Jun 2003 (UTC)

I agree with you about 10¹⁰. I wouldn't call the number of bits on a hard disk particularly large, either. It is certainly subjective. My point was that measurements of distance etc. are different from pure numbers. Measurements are, by definition, relative, whereas at least pure numbers are absolute. Largeness is another thing. Perhaps one definition would be "a number considered as large at a particular time by a particular culture". For example, I seem to remember that the Old Testament uses the number 40 as a generic large number in several places (e.g. "40 days and 40 nights"). -- Heron

Let me put this another way. I think the present article should be, as it mostly is, about the mathematics of large numbers. Other large quantities, such as astronomical distances, already have a place on the orders of magnitude pages (1e10 m etc.) Perhaps we should just link to them. -- Heron

Yes, you're quite right. Well, about most things. I could argue that physically distance is dimensionless but that would just be arrogant pedantry. The page title is "large number" not just "large", and the order of magnitude pages are pretty good for comparing distances. BTW did you see my reply for you on Wikipedia:Reference desk? -- Tim Starling 13:53 18 Jun 2003 (UTC)

World Almanac

What's special about the World Almanac year 2000?? Do any of you Wikipedians have an edition of the World Almanac year 2004?? Try it. 66.32.95.180 01:52, 27 May 2004 (UTC)

There's nothing at all special about it. It's a pretty lousy source, actually. But it's a source. But it was the only source I happened to have at hand for quattuordecillion, etc. If they're in the 2000 edition they're probably in the 2004 edition, too, but I didn't think it was appropriate to say "World Almanac" without identifying which edition, and I certainly didn't think it was appropriate to reference an edition I hadn't consulted.

I think these are in the Merriam-Webster Third and probably lots of other places. I may get around to making a trip to the library this weekend and finding out. Hopefully someone else will do it first. Dpbsmith 14:29, 27 May 2004 (UTC)

Examples

• <math>10^{\,\!100^{10}} < 10^{10^{20}}<math>
• <math>100^{\,\!10^{10}} < 10^{10^{10.3}}<math>

Also compare:

• <math>1.1^{\,\!1.1^{1.1^{1000}}} > 10^{10^{1.02*10^{40}}}<math>

I'm reverting the changes that were made to these equations, the discussion surrounding the equations clearly delineates the purpose of each and each is construed to show a certain aspect of "power towers", the revision is completely misleading when reading the text (besides making the equations wrong).

<math>10^{\,\!100^{10}}=10^{10^{11}} << 10^{10^{20}} <math>

<math> 100^{10^{\,\!10}} = 100^{10000000000}<math>

<math> 10^{10^{\,\!10.3}} \approx\ 10^{19952623149} = 100^{19952623149} <math> not even close

In the 1.1 problem, I simplified the last exponent, thus:

<math> 1.1^{\!1.1^{\,\!2.4699*10^{41}}} ? 10^{10^{1.02*10^{40}}} <math>

<math> 1.1^{24} \approx\ 10 <math> <math> 1.1^{1.1^{22}} \approx\ 10 <math>

thus:

<math> 10^{\!10^{\,\!2.4699*10^{41}}} > 10^{10^{1.02*10^{40}}} <math>

note that <math> 2.4699*10^{41} <math> is not larger than <math>2.4699*10^{41} - 46 <math> by enough to change the outcome of the main problem.

Dusty78 03:38, 12 May 2005 (UTC)

Dusty, I think you need to bone up on your high school algebra. (a^b)^c = a^(b*c) In particular,

<math>10^{\,\!100^{10}}=10^{10^{11}}<math>

is wrong. 100^10 is not equal to 10^11, it's equal to 10^20. Revolver 04:05, 12 May 2005 (UTC)

oops, right I've gone nuts spent too much time working out the rest to bother with checking all my work, still, the example doesn't really fit with the explination... oh well, I'm quitting while I'm behind Actually, I think I'll be reworking the probs untill I'm sure I'm right on the others..Dusty78 04:14, 12 May 2005 (UTC)

Ahh... Pride goeth before a fall... and screwy math before a bad post.... don't know what I was smoking ;) I'm just going to revert back to when it was actually right and correct the text 2nd example is wrong for same reason as first, 3rd is wrong but it took some actual number crunching to evaluate.Dusty78 04:25, 12 May 2005 (UTC)

sorry

Sorry, I wasn't thinking for a second about the relative errors of really large numbers. Hopefully the current explanation explains it well. Revolver 05:23, 13 May 2005 (UTC)