You can tell a fake mythmatician from a real mathematician
by this simple question: Is 0.999... equal to 1?
Of course 0.999... is not a number.
0.999... is a sequence of eight g l y p h s.
Glyph 1: "0"
Glyph 2: "."
Glyph 3: "9"
Glyph 4: "9"
Glyph 5: "9"
Glyph 6: "."
Glyph 7: "."
Glyph 8: "."
That sequence of glyphs is applied as a means of depicting
something in a way where the depiction is d e t e c t a b l e
b y those s e n s o r y o r g a n s that are related
to the visual sense (eyes).
The depiction detected by the organs of visual sensory in turn
is apperceived by the mind as the attempt of
r e p r e s e n t i n g in the context of
"written communication" an abstract/innate/absolute/empirical/
whatsoever c o n c e p t whereby the concept in question
- either is already known to the mind
- or is recognized by the mind as something currently unknown so
that clarification is needed
- or is about to be introduced to the mind by applying a method
of clarification.
(Methods of clarification are, e.g., explication, expatiation,
exposition, definition, declaration.)
The concept in turn is a means for r e f e r r i n g t o
an i t e m o f c o g n i z a n c e.
Methods of clarification are applied for assigning concepts to
items of cognizance. So that, e.g., in communication, the
concepts can be applied for referring to items of cognizance or
for introducing items of cognizance to communication partners.
During communication the concepts need to be "depicted" in a way
where the communication partners can detect the "depictions" by
means of their sensory organs. Concepts can, e.g., be "depicted"
in a way detectably by organs of acoustic sensory, e.g., by
means of sound waves denoting Morse code, by means of sound
waves denoting acoustic signals of alarm bells or sirens, e.g.,
by means of sound waves denoting spoken words in a specific
language. Concepts can, e.g., be "depicted" in a way detectably
by organs of visual sensory, e.g., by means of gestures, by
means of flares/luminous signals (traffic lights), by means of
glyphs representing letters of an alphabet, by means of glyphs
depicting visual symbols. ( E.g., the English-language-word
"scissors", the French-language-word "ciseaux", the
German-language-word "Schere" depict the same concept -- be
these words written or spoken. The same concept can also be
depicted by means of glyph number 34 (decimal) of the WingDings
font...)
In your postings you apply the sequence of glyphs "0.999..." in
order to convey some of your insights to the readers of the
newsgroup.
From the statements of some of the readers of the newsgroup one
can deduce that those readers do not agree with you.
Are you sure that the concepts depicted by you by
typing/applying the visually perceptible glyph-sequence
"0.999..." are the same concepts that are depicted by others when
they apply the same sequence of glyphs?
Are you sure that the concepts depicted by you by
typing/applying the visually perceptible glyph-sequence
"0.999..." do refer to exactly the same "item of cognizance" as
those concepts that are depicted by others when they apply the
same sequence of glyphs?
Ulrich