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Topic: 0.9999... = 1 that means mathematics ends in contradiction
Replies: 53   Last Post: Mar 18, 2013 9:33 PM

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 fom Posts: 1,968 Registered: 12/4/12
Re: 0.9999... = 1 that means mathematics ends in contradiction
Posted: Mar 13, 2013 5:42 AM

On 3/12/2013 10:24 PM, Virgil wrote:
> spermatozon@yahoo.com wrote:
>

>> On Wednesday, March 13, 2013 11:19:51 AM UTC+11, 1treePetrifiedForestLane
>> wrote:

>>> yes, and the proper infinite series with which
>>>
>>> it is to be compared, is the "real number,"
>>>
>>> 1.0000..., not omitting any of the zeroes
>>>
>>> on your little blackboard, dood.
>>>
>>>
>>>
>>> see Simon Stevins; *creation* of teh decimals,
>>>
>>> including this sole ambiguity, 15cce.
>>>
>>>
>>>

>>>> It s a symbol which represents an "infinite series",
>>>
>>>> which in turn is a sequence.
>>
>> yesw but .9999... is a non-finite number
>> and 1.0000.. is a finite number
>> thus
>> when maths shows
>> .9999... is a non-finite number = 1.0000.. is a finite number

>
> 0.9999... and 1.0000... are numerals (names of numbers), not numbers.
> They are only different names for the same number.
>

And, in addition, to say that 1.000... is
finite may also be arguable.

As names, decimal expansions are what they
are. 1.000... expresses a particular name
exactly. Without the full expression, one
must consider scenarios involving rounding
error. In that case, the finite representation
corresponds to an equivalence class of
decimal expansions that round to whatever
finite number of significant digits specifies
the system of finite abbreviation.

To say that 1.000... is finite without
qualification is to invoke a convention that
is not intrinsic to the system of names that
grounds the representation.

Of course, it is a common convention...

...that ought not invalidate mathematics.

Date Subject Author
3/8/13 byron
3/9/13 bacle
3/9/13 Pfsszxt@aol.com
3/12/13 Brian Q. Hutchings
3/12/13 byron
3/12/13 Brian Q. Hutchings
3/12/13 byron
3/12/13 Virgil
3/13/13 YBM
3/13/13 JT
3/13/13 Brian Q. Hutchings
3/14/13 JT
3/14/13 Brian Q. Hutchings
3/12/13 bacle
3/12/13 Virgil
3/13/13 fom
3/13/13 JT
3/13/13 JT
3/13/13 JT
3/13/13 fom
3/13/13 JT
3/13/13 JT
3/13/13 JT
3/13/13 JT
3/13/13 JT
3/13/13 fom
3/14/13 JT
3/14/13 fom
3/14/13 Brian Q. Hutchings
3/14/13 JT
3/14/13 JT
3/13/13 fom
3/13/13 JT
3/16/13 byron
3/16/13 JT
3/13/13 JT
3/14/13 Transfer Principle
3/15/13 JT
3/15/13 JT
3/15/13 JT
3/15/13 JT
3/15/13 JT
3/18/13 Brian Q. Hutchings
3/14/13 JT
3/14/13 fom
3/14/13 Brian Q. Hutchings
3/14/13 Brian Q. Hutchings
3/13/13 fom
3/13/13 JT
3/13/13 fom
3/13/13 JT
3/9/13 J. Antonio Perez M.
3/13/13 JT
3/15/13 harold james