Saturday, July 20, 2024

Opting out of the set theory

  1. It seems that several prominent mathematicians including Kroenecker objected to the set theory.
  2. Mathematics, physics and philosophy are academic and scholastic fields practiced by « learned doctors ». These professional are in competition to own academic subjects.
  3. The word « infinity » was owned by philosopher for millennia, but in the 19th century mathematicians « stole » infinity from philosopher and made infinity a mathematical object. Or at least they tried by using the set theory as false witness. To me they failed.
  4. The culprit is Herr Cantor. He initiated the sick process of incorporating the metaphysical concept of infinity into the precise science of mathematics. Mathematicians could not quantify infinity instead they transformed mathematics into metaphysics.
  5. Mathematics is about definitions.
  6. Any symbol in mathematics can be defined arbitrarily by other symbols.
  7. Mathematical definitions do not attribute « meaning » to the defined word. If they did, that would be physics not mathematics. In mathematics « a » can mean anything. It only has mathematical meaning as a quantity. In physics « a » can be « acceleration » or some other named quantity.
  8. For instance, we have a definition of number by Euclid as multiplicity of units...

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A new definition of subset

 1. I don't think it is necessary to have two words to indicate parts of a set, namely, subset  and proper subset . 2. Let's drop ...