Cantor's Diagonal Argument
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MATHEMATICS
Set Theory
Cantor's Diagonal Argument
A single clever twist revealed multiple sizes of infinity, reshaping mathematics forever
2 days ago
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What fundamental insight does Cantor's diagonal argument provide about infinite sets?
It shows that some infinite sets are too large to be matched one-to-one with natural numbers, proving the existence of uncountable infinities.
It proves that all infinite sets can be listed in a sequence like natural numbers, making them countable.
It demonstrates that infinite sets are all the same size, with no differences in their cardinality.
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MATHEMATICS
Set Theory
Cantor's Diagonal Argument
Cantor's diagonal argument reveals multiple sizes of infinity beyond natural numbers
10 Jan 2026
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What is the key step in Cantor's diagonal argument that proves the existence of uncountable sets?
Constructing a new element that differs from every element in a supposed complete list at the diagonal position
Showing that the natural numbers can be paired with real numbers one-to-one
Proving that infinite sets have the same size as finite sets
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