Re: rational or irrational?

In article <1119036683.821783.266310@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
<stush@xxxxxxxxxxxxxx> wrote:
>Arturo Magidin wrote:
>> In article <1118776531.165504.139090@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
>> Nurxgwkk <wildlife@xxxxxxxxxxx> wrote:
>> >is 0.00000000.....0000001 with and infinite amount of zeros in-between
>> >an irrantional number or not?
>>
>> Neither. In the real numbers, there is no such thing.
>
>Is it that simple?
>
>The square root of 2 is a real number, but its decimal expansion (as in
>a sequence of base 10 digits) does not exist in our universe. Yet the
>sequence of digits 0.000000...000001 does exist--you are looking at in
>on your screen right now! (try to type out the complete decimal
>expansion of sqrt(2)).

Nonsense. The "sequence" described claims that there is "an infinite
amount of zeros", allegedly "followed" by a 1. You may think you are
"seeing it on your screen", but then you are just deluding
yourself. You can have all zeros; you can have a finite number of
zeros and then a 1; but you cannot have "first" an infinite number of
zeros, and "then" a 1, and still be talking about a real number. it
has nothing to do with being able to write down something that
represents the number or not.

>Consider 0.33333...33333 where ... replaces an infinite amount of
>three's.

What you have written is nonsense as well, since you are saying that
"after" an infinite number of 3's, there will be five more 3's. That's
nonsense. You can talk about 0.3333.... (with the ellipsis being
understood as an infinite repeating sequence of 3's), though.

>Is this 1/3? I do not think this is a trivial question.

I do not think you know what you are talking about, so it seems hardly
a problem that you think something or other.

>My point here is infinite digits is not void in subjects of reals,

Nobody said it was. The point, however, is that there is no real
number in which you have "first" an infinite sequence of ->anything<-,
and ->then<- another digit.


--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes")
======================================================================

Arturo Magidin
magidin@xxxxxxxxxxxxxxxxx

.

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