Re: infinity

Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
> stephen@xxxxxxxxxx said:
>> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
>> > stephen@xxxxxxxxxx said:
>> >> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
>> >> > Randy Poe said:
>> >> >>
>> >> >> Tony Orlow (aeo6) wrote:
>> >> >> > because you claim there were balls in the vase, and then it became empty, and
>> >> >> > you are only removing 1 ball at a time, so there MUST have been a last ball
>> >> >> > removed. However, you cannot name that last ball removed, since there is always
>> >> >> > another to remove. If you DID name that last ball removed, the I can name 9
>> >> >> > times as many as have been removed that have not been removed. Don't you feel
>> >> >> > like you are trying so sail a big sponge across the sea? Do you wonder why it's
>> >> >> > such a drag?
>> >> >>
>> >> >> Can you name the last point between 0 and 1 which is less than 1?
>> >> >>
>> >> >> - Randy
>> >> >>
>> >> >>
>> >> > Binary 0.111...111
>> >> > Decimal 0.999...999
>> >>
>> >> What is (0.999...999+1)/2? Is it between 0.999...999 and 1?
>> >> Or is it undefined?
>> >>
>> >> Stephen
>> >>
>> > 000...000:000...000.999...999:500...000. Very good. You got half an
>> > infinitesimal out of me! ;D
>> > --
>> > Smiles,
>>
>> > Tony
>>
>> Is it between 0.999...999 and 1? If so, then 0.999...999 is
>> not the last point between 0 and 1 which is less than 1.
> 0.999...999 is the last first-level infinitesimal in the first unit. You have
> just dipped your toe into the second level of infinitesimals.

The question was about 'points'. Are second level infinitesimals
points or not? They apparently are located on your number
line between other points.

>>
>> If it is not between 0.999.999 and 1, then where is it?
> That's where it is, in between those two points which you consider identical.

So were you wrong when you claimed that .999...999 is the
last point between 0 and 1 that is less than 1? There
are apparently an infinite number of second level infinitesimals
between .999...999 and 1. And I imagine there are even
more third level, fourth level, etc level infinitesimals
lurking in your number line. Are all of these infinitesimals
points or not? If they are not points, what are they?

>> You are going to have to redo a lot of basic arithmetic
>> as x<y -> x < (x+y)/2 < y is a direct consequence of basic
>> arithmetic.
> That still holds.

Only because .999...999 is not the last point between 0 and
1 that is less than 1. I wonder if you are now able
to recognize that there cannot be a last point between 0 and
1 that is less than 1, unless you give up closure under
addition and division.

Stephen
.

Relevant Pages

  • Re: infinity
    ... >> 0.999...999 is the last first-level infinitesimal in the first unit. ... >> just dipped your toe into the second level of infinitesimals. ... The first one differs ...
    (sci.math)
  • Re: infinity
    ... >>> just dipped your toe into the second level of infinitesimals. ... The first one differs ... Tony? ...
    (sci.math)
  • Re: infinity
    ... >> just dipped your toe into the second level of infinitesimals. ... Second level infinitesimals are to points what points are to lines. ... negative dimensional objects. ...
    (sci.math)