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The continuum hypothesis is a mathematical conjecture about the possible sizes of infinite sets. It states that there is no set whose cardinality is strictly between that of the integers and the real numbers. Learn about its history, independence, and related topics.
22 Μαΐ 2013 · The continuum hypothesis (CH) is one of the most central open problems in set theory, one that is important for both mathematical and philosophical reasons. The problem actually arose with the birth of set theory; indeed, in many respects it stimulated the birth of set theory.
Continuum hypothesis, statement of set theory that the set of real numbers (the continuum) is in a sense as small as it can be. In 1873 the German mathematician Georg Cantor proved that the continuum is uncountable—that is, the real numbers are a larger infinity than the counting numbers—a key
3 Μαΐ 2021 · What is the continuum hypothesis? Very roughly speaking, the continuum hypothesis is a statement about the behaviour of certain infinite numbers — the so-called cardinals. The finite cardinals are very familiar: 0, 1, 2, 3, ... They provide answers to “how many?” -questions, such as “How many solutions does this equation have?”
2 ημέρες πριν · The continuum hypothesis is a proposal by Cantor that there is no infinite set with a cardinal number between that of integers and real numbers. It is undecidable in conventional set theory, but has been shown to be false by some axioms.
Notes to The Continuum Hypothesis. 1. See Hallett (1984) for further historical information on the role of CH in the early foundations of set theory. 2. We have of necessity presupposed much in the way of set theory.
The continuum hypothesis (CH) | the hypothesis or conjecture that 2@0 = @1 | is as old as set theory itself and has cast its long shadow over the discipline for the entirety of its history. As early as 1878, Cantor asked the question in its modern form: is every in nite X R in bijection with either. N or R?
