User talk:Asalmon

Peano's Axioms

Sorry but I'm not sure I agree with your edits here. My reasons are on the talk page. What's your views on this in light of my comments? --prime mover 16:21, 8 September 2011 (CDT)

Hint for tracking changes

If you make sure that any page you edit gets added to your watchlist, then any questions that are raised on the talk page of that page will automatically make sure you are notified. In that way it would not be necessary to specifically send you a message on your talk page that such-and-such a page has changed. --prime mover 00:35, 9 September 2011 (CDT)

Reinvention of wheels

One thing I would watch out for is the danger of recreating proofs which have already been done. I recommend you take some time out to study what already exists in the field that you're thinking of contributing to before you spend a lot of time creating proofs.

As an example, there is a massive wealth of simple results in Category:Set Theory and its subcategories which you shoud be able to use directly, rather than working through them again blow by blow. In particular there's Intersection with Subset is Subset which gives you $S \subseteq T \iff S \cap T = S$, which you proved again in Axiom of Subsets Equivalents.

Just a thought. --prime mover 13:53, 10 September 2011 (CDT)

Keep structure clean

When you add interesting little comments to pages, please try and keep them out of the "Proof" (or "Definition" or "Theorem" sections) as these are more-or-less formal expositions of subject matter. Asides are best inserted into "comment" or "also see" or "notes" or "warning" sections, or whatever is most appropriate.

The plan is to make the formal expositions of such a standard and quality that they can be interfaced with an automatic proofing system (probably years away yet, and no firm strategy yet). --prime mover 14:56, 11 September 2011 (CDT)

Set theory long term goal

I see where you're coming from, but (without having seen the book you're working from) I'd be surprised if there's much in there which isn't already up - I've already extracted a few books' worth of stuff. I would suspect that there's not a great deal in there which is genuinely "new" to ProofWiki as such, it's just that it may be structured differently, and spread over a number of pages.

In particular, the "proof by recursive definition" is already in place, as it's fundamental to all expositions of the definitions of the set of natural numbers. You can't avoid it. Just that in the context it's in, it's used to construct $\N$ from the concept of a naturally ordered semigroup, possibly an unusual way of proceeding, but no less rigorous for all that.

There is a genuine reason for it having been done that way. Definition pages should be just that, definitions. If there are immediate conclusions which can be drawn from those definitions, however trivial, they are placed in their own pages. In that way the ability to use a particular atomic result as a link on another page to provide the justification for a step in a proof becomes so much more straightforward.

If there are alternative definitions for existing stuff, then the usual technique is to add a separate section called "Alternative Definition(s)" or whatever, so as to keep the expositions clean.

Also, if a particular exposition is not incorrect, but just hasn't been put into the same format as you have in your book, then consider:

a) Leaving well alone, if the way you have it written does not add anything to the exposition

or:

b) Adding your way of doing it as an alternative, in a separate section again (preferred, if it is genuinely radical)

Also note the following. If there are genuinely different definitions for a given term, then from our perspective there is no "right" or "wrong" definition, just alternatives. ProofWiki has already gone down the path of having chosen one of these options, and (unless the definition which has *not* been chosen is genuinely and demonstrably "better", and by "better" I don't just mean "the one I learned in school") it is not in anyone's interest to go through and change everything to match the other definition. On the other hand, to add extra stuff based on the differences in definition *is* probably appropriate.

In that way ProofWiki becomes more than the sum of its parts.

Carry on with your plan, but (as I say) please be prepared to find that some of what you do gets reversed out because it's already in the database in a different form. --prime mover 03:10, 13 September 2011 (CDT)

Source works

Another thing you might want to do is take a look at what's done in the ProofWiki:Books page, and add the Quine book to it, filling out all the details like with other books we have in there. Use one as an example, perhaps E.J. Lemmon: Beginning Logic.

Bear in mind that Quine hasn't been added to the Mathematicians page yet - I'll try to get to it tonight. --prime mover 03:23, 13 September 2011 (CDT)

... that has now been done, and I've also set up the stub page for the book contents itself. Feel free to fill it in. --prime mover 14:14, 13 September 2011 (CDT)

Links to other pages

Some interesting results and a good start to establishing class theory.

However, a couple of things:

a) Please try to link to existing pages wherever possible. A case in point is Definition:Epsilon Relation which I looked at puzzled for a while till I realised that $\in$ means "is an element of".

b) Also, every page needs to be assigned to at least one category.

c) Certain statements are immediate consequences of the definition, and (particularly if one is completely familiar with the subject matter) it is tempting to just add them on the definition page, perhaps with some words along the lines of "this obviously follows". However, one of the purposes of this site is to be able to introduce concepts to those who may have not thought about the subject, and such statements are not obvious at all. Therefore, however trivial, all such statements are added as completely separate pages, linking to the definition page which would then have a link on the "Also see" section to that consequence. An example of this is the page Definition:Transitive Class.

I have going through some of your recent edits and amended as appropriate or added templates indicating work needed, so that you get the idea of how these things need to be presented. --prime mover 04:31, 26 November 2011 (CST)