User talk:Lord Farin

Thanks
Thanks for helping me set up Tarskis' Geometry, LF :) --GFauxPas 14:02, 24 January 2012 (EST)


 * Welcome. I've noticed that I can grasp and use new definitions and axioms at speeds greatly above average. It would just be selfish to keep that advantage to myself and not put it to good use ;). --Lord_Farin 14:06, 24 January 2012 (EST)


 * LF I'd like your help for the Axiom of Continuity. Though I understand the axiom itself, there are some concepts there that are too delicate for me. Namely,the author gives a presentation of the axiom as a 2nd-order statement or an axiom schema, while the information is (he claims) still expressible as a first order statement. I don't know how that works, and I'd appreciate your illumination of the matter once you get a chance to look at it. --GFauxPas 17:11, 24 January 2012 (EST)


 * As it stands, and if I read correctly, the second-order statement is subtly stronger than the schema (because not all sets can be defined in first-order logic; hence cannot be covered by first-order statements). However, first-order theories are quite important because they have a theorem (the Completeness Theorem) stating that if something is necessarily true in all models of a theory (like Tarski Geometry, or Set Theory), then you can prove it (!). See WikiPedia. This is not true for second-order theories. Lastly, the sets that first-order logic 'misses' can often be circumvented in some way, but at a price: theorems like Peano's Axioms Uniquely Define Natural Numbers fail when P5 is replaced by the corresponding first-order axiom schema. Hopefully, you could follow that. --Lord_Farin 17:37, 24 January 2012 (EST)
 * I didn't get everything in that paragraph but it helped me out, thanks! But what does the author mean that the axiom can be used in first order form, even though it's presented as second order? --GFauxPas 22:16, 24 January 2012 (EST)


 * I think he means that, if you are willing to pay the price I mentioned earlier, you can swap the second-order axiom for the schema to receive all benefits of the extensive theory on first-order logic (as this is the only axiom which is second-order). --Lord_Farin 02:59, 25 January 2012 (EST)

Hi there... anything else I should know
Hey there. I'm a new user, and I noticed you've been following along cleaning up my edits. Any chance you could add anything else that I should watch out for? I should be able to learn from the ones you've corrected, although I couldn't find a good guide on all the nitpicks around. Scshunt 03:20, 17 February 2012 (EST)


 * Sorry to butt in ... I take your point regarding "nitpicks". Some of the structuring does seem arbitrary and overly fussy, but there is method in our madness. One day we ought to make sure that all our nitpicks are gathered together on one page, but this has not happened yet (mea culpa).
 * In the meantime not to worry - tidying up is just something we do (well, me in particular) when nerving up energy for something that will take a considerable amount of hard work. --prime mover 07:20, 18 February 2012 (EST)


 * Sorry, I didn't meant that to come off badly. I consider myself to be a skilled picker of nits, much to the annoyance of those around me, so I'm not in the least annoyed that you want to maintain a consistent style. That's vital for making sure that the project doesn't become a mess. --Scshunt 01:47, 19 February 2012 (EST)


 * Skilled nickers of pits (oh wot-EV-er) are welcome. --prime mover 02:10, 20 February 2012 (EST)


 * You should check out Help:Editing; it contains most of house style. The most important thing is that it is strived for that all definitions get their separate pages, rather than one page containing a load of definitions. For example, you will see that I moved the definition of connectivity back to its own page. Feel free to ask if anything is unclear. Oh, and indeed, I prefer to answer a question on the same page, it's easier then to keep track of the conversation. --Lord_Farin 03:23, 17 February 2012 (EST)


 * Ok, thanks! Scshunt 03:25, 17 February 2012 (EST)