continuum hypothesis


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continuum hypothesis

n
(Mathematics) maths the assertion that there is no set whose cardinality is greater than that of the integers and smaller than that of the reals
References in periodicals archive ?
Cantor's research on sets and his creation of the continuum hypothesis, CH, in 1878 have become a perplexing problem for mathematicians with no complete and satisfactory solution.
The fourth problem is the Continuum Hypothesis, which concerns the comparability in size of infinite sets (some infinite sets are bigger than others, and it is unclear which is the second smallest).
There are questions that remain undecided by the accepted axioms of set theory (what Maddy calls the Independent Questions) that look as if they should have determinate answers; the most well-known example is Cantor's Continuum Hypothesis.
Many readers will be sympathetic to this continuum hypothesis, and recognize that it contrasts sharply with the old positivist picture of scientific reasoning, which tried unsuccessfully to find some special criteria demarcating scientific reasoning from ordinary reasoning that we apply in everyday life situations.
Still in typescript, this text contains the lecture notes for a course Cohen (1934-2007) taught at Harvard in spring 1965, shortly after his work on the continuum hypothesis.
In a famous lecture presented in 1900 at the International Congress of Mathematicians in Paris, Hilbert placed this assertion, called the continuum hypothesis, at the top of a list of the 23 most important mathematics problems of the new century.
Proving the truth or falsehood of Cantor's continuum hypothesis boils down to answering this: Where does the set of real numbers sit in the hierarchy of infinite sets?