Timeline for How to define tuples?
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 7, 2016 at 13:56 | comment | added | poizan42 | Rest assured that there are people who cares. Anyone designing systems for formal verification need to decide how to define tuples and if you decide to use set theory as your basic axioms then you need to decide how to define them as sets. | |
| Jan 27, 2010 at 8:03 | comment | added | Francesco Turco | @HarryGindi: I don't want to index by arbitrary complex numbers, but by natural numbers (seen as particular complex numbers). Just wanted to say I prefer not to index by "pure" natural numbers as defined through inductive sets. For example, I prefer to use the digit 0 for the complex number (0R,0R) and not for the empty set (0R stands for the zero defined as a dedekind cut or a cauchy sequence). This is because complex numbers and their operations are much more used in practice than "pure" natural numbers with addition and multiplication alone. | |
| Jan 27, 2010 at 3:37 | comment | added | Darsh Ranjan | This answer resonates closely with how I think. The concept of ordered tuple is essentially primitive. The fact that the structure can be implemented in pure set theory is mildly interesting, but it's no fundamental insight into the nature of tuples. | |
| Jan 26, 2010 at 20:26 | comment | added | Harry Gindi | Wait, that's pointless, Francesco. Why would you want to index by complex numbers? They're not ordered and don't admit any nice type of order structure. You're better off indexing by an arbitrary set of cardinality the continuum. Hell, the only reason we index by naturals is because they're well-ordered and it's easy to see where everything starts. Also with the natural numbers, induction by successor holds up to $\aleph_0$. Sometimes you'd like to index by posets like when taking projective and inductive limits, but you would never want to index by complex numbers. No way. | |
| Jan 26, 2010 at 16:41 | comment | added | Francesco Turco | I would use ordered pairs and sets of ordered pairs in a "temporary" manner, only to define the various number systems up to the complex numbers, and then I would "forget" them in favour of n-tuples (where n is a complex number) and sets of n-tuples. Also, as you correctly pointed out, there are at least five versions of the number 3, but four of them are "temporary", and only the latest one is the "real", useful one. But I think in set theory the procedure to define something is at least as important as the thing you define, so you cannot really skip that step. | |
| Jan 26, 2010 at 14:14 | history | answered | Harald Hanche-Olsen | CC BY-SA 2.5 |