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What does unsolvability mean?

Looking for the meaning or definition of the word unsolvability? Here's what it means.

Noun
  1. The property of being unsolvable.
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This led to work by many mathematicians to further explain the theory and philosophy of mathematical unsolvability in terms of logic or other models of mathematics.
Many of the results listed in this table are the direct consequence of implications concerning the unsolvability or solvability of certain problems.
In particular, he proved the unsolvability of the halting problem.
I think this is an unsolvable problem, and I might start with an attempted proof of its unsolvability rather than a solution.

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