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Correct. ZF is anything but realistic. It is just nice for creating mathematical theories, which can indeed be wonderful and also very useful for our world.
by giomasce 10y ago
Correct. ZF is anything but realistic. It is just nice for creating mathematical theories, which can indeed be wonderful and also very useful for our world.
- Smaug123 10y agoMy experience is limited, but I consider that to be why the Continuum Hypothesis isn't very interesting. The continuum is how we try and embed "space" into ZFC, but the way we embed has certain freedoms in it: one of which being the size of the set that is used to represent the continuum. It's the same kind of uninteresting as the difference between the two implementations {x, {x, y}} and {{x}, {x, y}} of the ordered pair.