2 ms·
> Guess it's not. Isn't there a theorem that speaks of the existence or non-existence of a set whose cardinality is strictly larger than Q and strictly smaller
by ur-whale 7y ago
> Guess it's not.
Isn't there a theorem that speaks of the existence or non-existence of a set whose cardinality is strictly larger than Q and strictly smaller than R.
And a conjecture that says this theorem might well be unprovable?
- pdonis 7y agoA "theorem" is a proved proposition, so there is no such thing as a theorem that might well be unprovable. The proposition you refer to (which is not a theorem since no proof is known, and in fact it has been shown that this proposition is logically independent of the usual foundations of set theory, so it cannot be proved in that framework) is called the Continuum Hypothesis: https://en.wikipedia.org/wiki/Continuum_hypothesis https://en.wikipedia.org/wiki/Continuum_hypothesis
- lonelappde 7y agoThe theorem is that the continuum hypothesis is independent of ZFC.
- BeetleB 7y agoIn this particular case, though, that is irrelevant. This set is strictly of the same cardinality as the rationals.