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Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: Axiom of choice and the three spheres.
Replies: 20   Last Post: Dec 3, 2006 4:58 AM

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Gauster

Posts: 79
Registered: 9/14/06
Re: Axiom of choice and the three spheres.
Posted: Dec 2, 2006 2:29 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

> Measure is additive. Who would
> expect non-measurable sets assembled into a
> measurable
> set to always have the same measure? Nothing
> paradoxical there.

People who have stick the physical image of a sphere in their minds might find it paradoxical. They think in terms of points in the three dimensional space, picturing the common physical space of daily experience, and that's what causes the conflict, either with BT or the fact that a segment has as many points as a square.

Perhaps abandoning the naive intuition of points in physical space and correspondence between space continuity and real numbers would handle all kind of counterintuitive results.

>
> --
> Michael Press

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