continuum hypothesis
The "continuum hypothesis" is a central question in set theory, proposed by Georg Cantor, concerning the sizes of infinite sets.
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Definition
C2Set Theory
(technical, academic)A proposition stating there is no set with a size between that of the integers and the real numbers.
Example
- The continuum hypothesis remains one of the most famous unsolved problems in mathematics.
- Understanding the continuum hypothesis is crucial for advanced studies in set theory.
C1Physics and Continuum Mechanics
(technical)An assumption that a material is continuous and not composed of discrete particles for the purpose of mathematical modeling.
Example
- In continuum mechanics, the continuum hypothesis allows us to treat materials as continuous masses.
- The continuum hypothesis simplifies the equations used in fluid dynamics.