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I didn't claim that FTA is the most practical way to perform Gödel numbering. I just said that it's my favorite application of it, in a general sense, not that
by curiousgal 10y ago
I didn't claim that FTA is the most practical way to perform Gödel numbering. I just said that it's my favorite application of it, in a general sense, not that I'd use it to do so. Preferences are subjective.
- kazinator 10y ago"Application" in mathematics usually means that something is used as a necessary component of a solution in another area. If Gödel numbering is an "application" of the FTA, that strongly suggests that you're saying that FTA somehow enables the possibility of Gödel numbering, or else that it is exploited somehow to endow that numbering with convenient properties (without loss of generality). Is that true?
- curiousgal 10y agoYes, exactly. The reason I said that is because Gödel himself used FTA to build his observation (Göodel numbering).
- JadeNB 10y ago> "Application" in mathematics usually means that something is used as a necessary component of a solution in another area. I think that sentence is entirely true if you delete the word 'necessary', and otherwise entirely false. I think that almost everyone would agree that at the heart of modern cryptography is an application par excellence of modular arithmetic, but I think that no-one would claim that cryptography cannot be done without modular arithmetic.