Re: Positive random number

In article <ebd1c529-c0fa-4e17-96e3-08ce9d73fb6f@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
<jameskuyper@xxxxxxxxxxx> wrote:
I'm familiar with this meaning for "almost all", and I think you've
misapplied it. I don't remember the precise definition, but I believe
that the entire set has to be infinitely bigger than the set of
exceptions. For instance, a function that is 0 for all real values,
except that it is 1 for all integers, then that function is 0 "almost
everywhere". I don't believe that the set of mathematicians is
infinitely larger than the subset who hold those opinions.


"Almost all non-negative even numbers less than 1 google are non-prime."

Is "1 google" infinite? No. Is the statement true? I think nearly
everyone (who knows what prime numbers are) would agree that it is
true.

"1 google" is close enough to "infinity" for -practical- purposes as to
make no difference, but I -believe- that if you change "google"
to "million" or even "thousand" that very close to the same number
of people would continue to agree that the modified statement is true.

I believe if you reduced the number down to 20 that the disagreement
rate would be very nearly the same; even at 11 I don't think the
disagreement rate would be significantly higher.

Now, if you reduced the limit to 3 then I could imagine people
getting bothered about the wording, since "almost all" in that case
would be empty. At 4 or 5 then the "almost all" sample size would
be the same as the size of the alternative and people might still
get flustered about the wording. But I believe that one single
exception out of a relatively small set would still broadly be agreed
as the rest being "almost all". I suspect that the psychology of
"almost all" gets more muddy when there are multiple exceptions.
--
We regret to announce that sub-millibarn resolution bio-hyperdimensional
plasmatic space polyimaging has been delayed until the release
of Windows Vista SP2.
.

Relevant Pages

  • Re: Logarithm of transfinite numbers
    ... up to and including that natural number cannot be infinite. ... Wording like, "at the end of all points" would get me excoriated. ... TO seems to be saying that if you can't tell it is infinite by looking ... naturals, you have to look at the whole, not merely at some part. ...
    (sci.math)
  • Re: Infinite Meet or no-meets
    ... infinite subset of that set such that either all the people in the ... consists only of three people. ... We have an infinite subset where every member has not met all the ... Perhaps the problem is the wording. ...
    (sci.math)
  • Re: [PATCH 2.6.21-rt2] PowerPC: decrementer clockevent driver
    ... My wording was sloppy. ... Some CPUs have the DEC exceptions basically edge triggered (yeah I know ... That's why, among others, the IRQ soft-disable code has code ...
    (Linux-Kernel)