On 12/16/2013 11:44 PM, LizR wrote:
On 17 December 2013 20:34, meekerdb <meeke...@verizon.net <mailto:meeke...@verizon.net>> wrote:

    On 12/16/2013 11:26 PM, LizR wrote:
    On 17 December 2013 19:01, meekerdb <meeke...@verizon.net
    <mailto:meeke...@verizon.net>> wrote:

        I know.  I was just taking 10^80 to mean "a very big number" which of 
        depends on context.  I generally do applied physics and engineering and 
        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, 
    though it is the same when used physically "for all intents and purposes" - 
    we already know that 10^80 is divisible by 10 (how did I work that, out 
    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 
    in the universe was 10^88, would you then know that the number of protons 
    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 reasons.

While the properties of the number 10^88 are mathematical facts, and their truth or falsity can be determined by calculation.

Some have proposed that as the defining difference between "real" and "mathematical"; you can know things exactly and certainly about the latter.

    Notice that it's a trick question.

I'm not sure. Did I miss something?

Probably not. Just that a very big number like 10^80 is effectively divisible by any small number, since the remainder can be neglected.


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