CONTINUUM HYPOTHESIS Meaning and
Definition
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The continuum hypothesis is a concept in set theory that was first proposed by mathematician Georg Cantor in 1878. It is a statement about the size or cardinality of sets that comprise the real numbers. According to Cantor's hypothesis, there is no set whose cardinality is strictly between that of the set of integers and the set of real numbers.
In other words, the continuum hypothesis suggests that there are no sets with a cardinality larger than that of the integers but smaller than that of the real numbers. It posits that the real numbers form the "smallest" uncountable set. If the continuum hypothesis is true, it means that there are no sets of numbers that are neither countable nor as large as the real numbers.
The significance of the continuum hypothesis lies in its implications for the foundations of mathematics. It pertains to questions about infinite sets and their different sizes or cardinalities. The hypothesis became one of the most prominent unsolved problems in set theory until 1963 when mathematician Paul Cohen showed that it cannot be proven or disproven within the standard axioms of set theory, known as Zermelo-Fraenkel set theory.
The continuum hypothesis has continued to generate interest and research as mathematicians explore its consequences and implications for set theory, logic, and the understanding of infinite collections.
Common Misspellings for CONTINUUM HYPOTHESIS
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Etymology of CONTINUUM HYPOTHESIS
The term "continuum hypothesis" is derived from Latin and Greek origins.
The word "continuum" comes from the Latin word "continuus", meaning "continuous" or "uninterrupted". It was first introduced by the German mathematician Georg Cantor in the late 19th century to describe certain uncountable sets, specifically referring to the real numbers as a continuous line without gaps or jumps.
The word "hypothesis" comes from the Greek word "hypothesis", meaning "a placing under" or "supposition". In mathematics, it refers to a proposition or assumption that is yet to be proven or disproven.
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