Talk:Union with Relative Complement
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Do you really need to bother with universal generalisation? Definition:Subset is just (broadly speaking):
- $(x \in S \implies x \in T) \implies S \subseteq T$
If we needed to bother with universal generalisation in every proof we'd never get anything done. --prime mover 16:50, 7 December 2011 (CST)
- I don't know, when do you think it is needed? I haven't seen it explicitly in any proofs on PW. You know the wiki better than I do, and as I said on my user page I won't be offended if you change it. --GFauxPas 16:57, 7 December 2011 (CST)
- Once we've got past all the work on predicate calculus as a formal system (which hasn't been done yet), it's not really needed at all. That's why it's never been used. It's used during the course of being able to justify hte picking of an arbitrary element and proving it has a particular property. You haven't seen it used in any proofs in PW because it's not needed. It would be like every time you needed to do some arithmetic on anything, having to justify it by appealing to the fact that the real numbers form a group under addition. --prime mover 17:07, 7 December 2011 (CST)
- Fine with me. Thank you for teaching me this. --GFauxPas 17:10, 7 December 2011 (CST)
- Once we've got past all the work on predicate calculus as a formal system (which hasn't been done yet), it's not really needed at all. That's why it's never been used. It's used during the course of being able to justify hte picking of an arbitrary element and proving it has a particular property. You haven't seen it used in any proofs in PW because it's not needed. It would be like every time you needed to do some arithmetic on anything, having to justify it by appealing to the fact that the real numbers form a group under addition. --prime mover 17:07, 7 December 2011 (CST)