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What is the singular of unsolvabilities?

What's the singular form of unsolvabilities? Here's the word you're looking for.

Answer

The noun unsolvability can be countable or uncountable.

The singular form of unsolvabilities is unsolvability.

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Examples
Many of the results listed in this table are the direct consequence of implications concerning the unsolvability or solvability of certain problems.
I think this is an unsolvable problem, and I might start with an attempted proof of its unsolvability rather than a solution.
In particular, he proved the unsolvability of the halting problem.
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.

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