On 17 December 2013 20:34, meekerdb <meeke...@verizon.net> wrote:
> On 12/16/2013 11:26 PM, LizR wrote:
> On 17 December 2013 19:01, meekerdb <meeke...@verizon.net> wrote:
>> I know. I was just taking 10^80 to mean "a very big number" which of
>> course depends on context. I generally do applied physics and engineering
>> and so 10^80+1 = 10^80 for physical variables.
> That reminds me of a joke...
> ...but you've probably heard it already, so I will stick to the point.
> 10^80 + 1 may happen to be a prime number (I leave the proof (or
> disproof) up to Stephen Paul King as an exercise in applied mathematical
> reasoning) in which case it is very different from 10^80 in terms of its
> mathematical properties, even though it is the same when used physically
> "for all intents and purposes" - since we already know that 10^80 is
> divisible by 10 (how did I work that, out without even being able to
> imagine 10^80 objects? It's like magic...! :)
> Which is a true statement in mathematics. But suppose I said the number
> of protons in the universe was 10^88, would you then know that the number
> of protons was divisible by 10?
No, because you couldn't truthfully make that statement (except by
accident). You don't know the number of protons in the universe, which is a
physical fact that could only be determined by measurement, not to mention
a far greater knowledge of cosmology than we currently possess (e.g.
whether the universe is infinite). And the measurement would be impossible,
except perhaps to within an order of magnitude, for all sorts of practical
While the properties of the number 10^88 are mathematical facts, and their
truth or falsity can be determined by calculation.
> Notice that it's a trick question.
> I'm not sure. Did I miss something?
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