21. The existence of Specker sequences has consequences for computable analysis. 22. The proof uses a particular fact about computable real numbers. 23. Experimental outcomes are not necessarily computable using the postulates of the theory. 24. To actually develop analysis over computable numbers, some care must be taken. 25. One can formally define functions that are not computable . 26. Every computable number is arithmetical, but not every arithmetical number is computable. 27. Every computable number is arithmetical, but not every arithmetical number is computable . 28. The set of computable numbers has the same cardinality as the natural numbers. 29. This means that the correlation functions are all computable from as Gaussian averages: 30. The image of a computable set under a total computable bijection is computable.
