2013/1/11 Jukka K. Korpela <[email protected]> > 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 > LaTeX Symbol List > ftp://ftp.funet.fi/pub/TeX/**CTAN/info/symbols/** > comprehensive/symbols-a4.pdf<ftp://ftp.funet.fi/pub/TeX/CTAN/info/symbols/comprehensive/symbols-a4.pdf> > which describes, in clause “3 Mathematical Symbols”, some notations used > for contradiction. None of them resembles much the symbol in the image. > What comes closest is \blitza, but it’s still rather different, and there > is no information of what it might be in Unicode terms. > 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
