On 12/16/2013 11:44 PM, LizR wrote:
On 17 December 2013 20:34, meekerdb <[email protected] <mailto:[email protected]>>
wrote:
On 12/16/2013 11:26 PM, LizR wrote:
On 17 December 2013 19:01, meekerdb <[email protected]
<mailto:[email protected]>> 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
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.
Brent
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