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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: > In article <f93df84bf04d434c832ed458c0df9b2c@googlegroups.com>, > 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 nonfinite number >> and 1.0000.. is a finite number >> thus >> when maths shows >> .9999... is a nonfinite number = 1.0000.. is a finite number >> it ends in contradiction > > 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.

