A consequence of the continuum hypothesis is that every infinite subset of the real numbers either has the same cardinality as the integers or the same cardinality as the entire set of the reals. ==Independence from ZFC== Cantor believed the continuum hypothesis to be true and tried for many years to prove it, in vain {harv|Dauben|1990}. It became...
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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 ... [9 related articles]
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In 1874 Georg Cantor discovered that there is more than one level of infinity. The lowest level is called countable infinity; higher levels are known as uncountable infinities. The natural numbers are an example of a countably infinite set and the real numbers are an example of an uncountably infini...
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a conjecture of set theory that the first infinite cardinal number greater than the cardinal number of the set of all positive integers is the cardinal number of the set of all real numbers.
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