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    Adding recursive irrationals to the rationals still leave... — Carmelics
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    Supports→Recursive irrationals alone are insufficient to fill all gaps in the real number line.

    Adding recursive irrationals to the rationals still leaves gaps in the continuum.

    Modality & PossibilityTruth & Knowledge
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    Recursive irrationals alone are insufficient to fill all gaps in the real number...Therefore, lawless irrationals must also be introduced to complete the mathemati...

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    Related propositions within the same area of thought.
    Recursive irrationals alone are insufficient to fill all gaps in the r...80%Lawless and pseudo-irrationals are needed for the mathematical continu...79%There must be gaps between the rational numbers that require filling w...78%Therefore, lawless irrationals must also be introduced to complete the...77%

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    SEP: wittgenstein-mathematics
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    The problem, as Wittgenstein sees it, is that mathematicians, especially foundationalists (e.g., set theorists), have sought to accommodate physical continuity by a theory that ‘describes’ the mathematical continuum (PR §171). When, for example, we think of continuous motion and the (mere) density of the rationals, we reason that if an object moves continuously from A to B, and it travels only the distances marked by “rational points”, then it must skip some distances (intervals, or points) not

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