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Instead of using colour or fluorescence variation, Ikezoe et al. exploited a rather different method of reporting on environmental changes by developing synthetic 'swimmers' that are sensitive to chemical gradients on the macroscale (Fig. 9) [98].
A key method in the usual proofs of the first incompleteness theorem is the arithmetization of the formal language, or Gödel numbering: certain natural numbers are assigned to terms, formulas, and proofs of the formal theory F. There are different ways of doing this; one standard approach is sketched here (for a rather different method of coding, see, e.g., Boolos & Jeffrey 1989).
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CEO of Professional Science Editing for Scientists @ prosciediting.com