continuum hypothesis

名词 n.
中文释义

英文释义

名词 n.
  1. The hypothesis which states that any infinite subset of ℝ must have the cardinality of either the set of natural numbers or of ℝ itself.
    — In other words, it is consistent with the axioms^([of set theory]) to suppose that the continuum hypothesis is false. (It had been known for some time — see below — that it is consistent with the axioms of set theory to suppose that CH is true.)
  2. The assumption, for the purposes of mathematical modelling, that the material being studied is a continuous mass rather than being composed of discrete particles.
    — Under the continuum hypothesis, the material being studied, whether it be solid liquid or gas, is assumed to be continuous.
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