* All calculations carried out on a Turing Machine
* The majority of mathematical statements and calculations given in maths textbooks

Some examples of mathematical statements that are not computable include:

* Calculations or statements which are ill-defined, such that they cannot be unambiguously encoded into a Turing machine: ("Paul loves me twice as much as Joe").
* Problem statements that appear to be well-defined, but for which it can be proved that no Turing machine exists

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