Not all infinite sets have the same cardinality. — Carmelics

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Not all infinite sets have the same cardinality.

Modality & Possibility Truth & Knowledge

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1 reason for

2 reasons against

Reasons For

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Reason for

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1.The positive real numbers have a greater cardinality than the positive integers.
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2.Both the positive real numbers and the positive integers are infinite sets.
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Reasons Against

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Reason against 1 of 2

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1.Predicativist mathematicians like Poincaré and Weyl reject impredicative definitions, which underlie the construction of the real number continuum.
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2.Without a predicatively acceptable construction of the reals, the claim that ℝ constitutes a well-defined set of greater cardinality than ℕ cannot be established.
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3.If the supporting argument's first premise relies on an illegitimate mathematical object, the comparative cardinality claim loses its primary evidential basis.
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Reason against 2 of 2

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