2016年9月22日木曜日

19 Incompleteness Theorem

19 Incompleteness TheoremWhat is the Universe?】Dialogue with the Universe

The proposition which cannot judge correction exists.
・・・Gödel (Kurt Gödel, Austria 1906-78) proved in 1930.
・・・Then, Turing(Aan Mathison Turing, UK 1912-1954) proved that there is no unific method of confirming beforehand whether a certain proposition is a proposition which cannot judge truth.
Reference: 「世にも美しい数学入門」Masahiko FujiwaraYouko Ogawa(p.147151)

If there is a proposition which cannot confirm that verification is impossible and it is unverifiable, it can say, "Search is eternal."
 ・・・Although nothing may remain even if it continues search throughout life・・・

Mathematical history
About 7000 years ago  Number was born. (Mankind began to group living.)
16th century    Imaginary number is accepted.
・・・"Forgetting the mental anguish received with imaginary number, and merely introducing this." Gerolamo CardanoItaly 15011576
17th century  Minus is accepted in Europe.
・・・Descartes draws a number line.   René DescartesFrance 15961650
The first half of the 19th century  An imaginary number is denoted by an axis of coordinates.complex plane  Carolus Fridericus GaussGermany 17771855
1935  Gödel's Incompleteness Theorem

・・・Then, Turing(Aan Mathison Turing, UK 1912-1954) proved that there is no unific method of confirming beforehand whether a certain proposition is a proposition which cannot judge truth.

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