“On Non-Computable Functions”, 1962-05-01 (; backlinks):
[On the Busy Beaver function.] The construction of non-computable functions used in this paper is based on the principle that a finite, non-empty set of non-negative integers has a largest element. Also, this principle is used only for sets which are exceptionally well-defined by current standards. No enumeration of computable functions is used, and in this sense the diagonal process is not employed.
Thus, it appears that an apparently self-evident principle, of constant use in every area of mathematics, yields non-constructive entities.
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