Mathematical Logic

Created2025-01-31|Updated2025-02-02|笔记数学

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Mathematical Logic

Common symbols of mathematical logic: , , , , .

Set Theory

We take a set to be an assemblage of definite, perfectly distinguishable objects of our intuition or our thought into a coherent whole.
— Georg Cantor

Cantor, the great creator of set theory, put forward basic assumptions of set:

A set may consist of any distinguishable objects.
A set is unambiguously determined by the collection of objects that comprise it.
Any property defines the set of objects having that property.

Wonderful thoughts though it is, native or Cantorian set theory is a weirdo behind its seemingly beautiful mask.

Russell paradox: : “ is not an element of itself”. is not a set.

How to solve it? Mathematicians, to say, gave up some degree of university and turned to axiomatic set theory i.e. confined ourselves.

We have “” which has no definition.

What does mean? Just short form of the proposition .

math set theory mathematical logic

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