From: Philippe Verdy <verdy_p_at_wanadoo.fr>

Date: Fri, 11 Jan 2013 20:01:14 +0100

Date: Fri, 11 Jan 2013 20:01:14 +0100

2013/1/11 Jukka K. Korpela <jkorpela_at_cs.tut.fi>

*> The page http://en.wikipedia.org/wiki/**Contradiction<http://en.wikipedia.org/wiki/Contradiction>(which isn’t particularly convincing or otherwise important) refers to the
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*> LaTeX Symbol List
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*> ftp://ftp.funet.fi/pub/TeX/**CTAN/info/symbols/**
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*> comprehensive/symbols-a4.pdf<ftp://ftp.funet.fi/pub/TeX/CTAN/info/symbols/comprehensive/symbols-a4.pdf>
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*> which describes, in clause “3 Mathematical Symbols”, some notations used
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*> for contradiction. None of them resembles much the symbol in the image.
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*> What comes closest is \blitza, but it’s still rather different, and there
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*> is no information of what it might be in Unicode terms.
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*>
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In fact what is expressed is not a contradiction, but a symbol for FALSE

(opposed to TRUE).

But mathemetics also include assertions that are neither FALSE or TRUE but

UNDECIDABLE (and it can be PROVEN that such assertion is undecidable,

within a logic system with its axioms, whiuch means that you can derive two

distinct logic systems where the undecidable assertion is arbitrarily set

as TRUE or FALSE).

There's also the need to express cases where assertions have any other

probability of being TRUE or FALSE (instead of just 0% and 100%), and

you'll need a symbol to express this probability, because it is sometimes

computable, within the logic system itself. Sometimes this probability is

not absolute and could be within a range (the UNDECIDABLE state means that

the probability range is [0%..100%] inclusively). This includes cases like

the results of some operations supposed to return any number, where you'll

need the concept of "NaN" (not a number), and even some more ranges of NaN

values indicating the cause of this undecidability.

Mathematics have a lot of logic (and numeric) systems (in fact their

possible number is most probably infinite). For each of them, you need more

symbols to express your assertions. How many symbols will you need ? Each

mathemetical theory studying one of them will then need to create its own

symbols

Received on Fri Jan 11 2013 - 13:03:50 CST

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