uncountable set


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uncountable set

[¦ən′kau̇nt·ə·bəl ′set]
(mathematics)
An infinite set which cannot be put in one-to-one correspondence with the set of integers; for example, the set of real numbers.
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The set author has just defined above is an uncountable set.
On the other hand, the real line is a visual representation of an uncountable set that corresponds with P(N).
KEY WORDS: Uncountable sets, APOS, metaphor, power set, natural numbers, mental images.
Explicitly, undergraduate mathematics majors study uncountable sets in Introduction to Proof or Transition courses and again in Analysis courses and upper division courses on set theory.
Participation in these courses and in many other situations in the field of mathematics should lead to constructions of new mental structures for dealing with uncountable sets.
Moreover, no source of which we are aware considers the development of mental structures for uncountable sets such as P(N).
The authors suggest that if there is no apparent mental process underlying one's conception of a set, as may be the case with uncountable sets, the meaning of "all" is not entirely clear.