Points in a Line, Plane & Space: Cardinality Comparison

Thread starter mprm86
Start date Apr 20, 2005
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Cardinality Comparison Line Plane Points Space

AI Thread Summary

The discussion centers on the concept of cardinality, specifically comparing the number of points in a line, a plane, and space, asserting that they all have the same cardinality, which is the cardinality of the continuum. Participants emphasize the importance of understanding the definition of "same number" in terms of cardinality. A key point raised is that while the cardinalities of these geometric constructs are equal, there are sets with cardinalities greater than the continuum, such as the power set of the real numbers. The conversation also touches on foundational concepts in set theory and the implications of different cardinalities. Overall, the discussion highlights the complexities of comparing infinite sets and their cardinalities.

Apr 20, 2005

mprm86

Show that they are the same number of points in a line, in a plane and in the space.
I have one more question: Which set has a cardinal number greater than the continuum. Why?

Thanks in advance.

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Apr 20, 2005

Hurkyl

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Sounds like homework. Have you had any thoughts on it? Know any useful facts about cardinality?

Apr 21, 2005

HallsofIvy

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Homework Helper

Start by writing out the DEFINITION of "same number"!

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