I'm explorating the Peano axioms > in the context of first or second order logic. > > Peano uses a "e." symbol > to express phrases like "x e. NN", > "x is a number". There was no set theory > intent in his m'indiquer. So I'd like to reuse the > material in set.mm related to > e., class variables, class builder. They > are in the set theory part, > but it seems to me they don't use > any set theory axiom. >
I was unsuccessful finding reliable historical information about Peano's epsilon. For example, Wikipedia https://en.wikipedia.org/wiki/Epsilon says 'The symbol \in, first used in set theory and logic by Giuseppe Peano and now used in mathematics in general for set membership ("belongs to") did, however, evolve from the letter epsilon, since the symbol was originally used as an abbreviation for the Latin word "est" ["is"].' First, I didn't know Peano was actually doing "set theory". Was he? Also, if it 'was originally used as an abbreviation for the Latin word "est"' then who was the original user? Presumably it wasn't Peano, since he was doing "set theory" per Wikipedia. If we assume, contrary to Wikipedia, that it was Peano who introduced epsilon as its first user, and that he was using epsilon to abbreviate "est", then perhaps he just meant "a property" and not "an element of". For example, "the apple epsilon green" might have just meant "the apple is green" as in ordinary conversation, not necessarily conceptualizing it as the apple being a member of the set of all green objects. And "A epsilon NN" might have simply meant "A has the property of being a natural number" rather than "A is a set contained in the larger set NN". All of that is my guess, though. If someone has better access to historical sources, please feel free to correct me. Norm -- You received this message because you are subscribed to the Google Groups "Metamath" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/metamath/dee27b9e-2e88-4ddb-887d-5e1b6f52618b%40googlegroups.com.
