But he was not able to prove this continuum hypothesis, and nor were many mathematicians and logicians who followed him.
This way they show that the problem of learnability is equivalent to the continuum hypothesis.
They authors go on to show that if the continuum hypothesis is true, a small sample is sufficient to make the extrapolation.
The mathematicians, who were working on a machine-learning problem, show that the question of ‘learnability’ — whether an algorithm can extract a pattern from limited data — is linked to a paradox known as the continuum hypothesis.
The findings will probably be important for the theory of machine learning, he adds, although he is “not sure it will have much impact on the practice”.
Therefore, the learnability problem, too, is in a state of limbo that can be resolved only by choosing the axiomatic universe.
Gödel showed that the statement cannot be proved either true or false using standard mathematical language.
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