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    A 3-sphere, like its 2D analogue the ordinary sphere, per... — Carmelics
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    Supports→The universe can be finite and unbounded at the same time, refuting the conflation of unboundedness with infinitude.

    A 3-sphere, like its 2D analogue the ordinary sphere, permits indefinite travel without boundary while possessing finite volume, making finite-yet-unbounded space formally coherent.

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    Key Terms

    2D analogue(as used in mathematics and geometry)
    A simpler, lower-dimensional version of something that works the same way—like how a circle on paper is the 2D version of a sphere in real life.
    3-sphere(as used in geometry and cosmology)
    A four-dimensional version of a sphere—just like a regular sphere is a 2D surface wrapped around 3D space, a 3-sphere is a 3D surface wrapped around 4D space that we can't easily visualize.
    Finite volume(as used in geometry)
    Having a measurable, limited amount of space inside—you could theoretically measure how much 'stuff' fits in it.
    Finite-yet-unbounded space(as used in cosmology and the philosophy of space)
    A space that has a limited total size but lets you travel infinitely without ever reaching an edge (like traveling around Earth: it's not infinite, but you never hit a boundary).

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    Formally coherent(describes the quality of completed infinities in Cantor's system)
    Logically consistent and free from contradictions when you work through the math or reasoning carefully, so it doesn't break its own rules.
    Without boundary(as used in topology and cosmology)
    Having no edges or endpoints—you could travel forever in any direction without hitting a wall or the 'end' of the space.

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    2 topics

    Truth & Knowledge1 linkedModality & Possibility1 linked

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    The universe can be finite and unbounded at the same time, refuting the conflati...

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