Palnot

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Hello, Palnot, and welcome to Wikipedia! Thank you for your contributions. I hope you like the place and decide to stay. Here are some pages that you might find helpful:

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I hope you enjoy editing here and being a Wikipedian! Please sign your messages on discussion pages using four tildes (~~~~); this will automatically insert your username and the date. If you need help, check out Wikipedia:Questions, ask me on my talk page, or ask your question and then place {{helpme}} before the question on your talk page. Again, welcome! RJFJR (talk) 15:05, 18 January 2008 (UTC)

Let me also welcome you. I noticed you edited the references in several math articles. This is an area where many articles can use improvement, so thanks. You might be interested in the mathematics wikiproject and its list of resources for new editors.

By the way, I noticed you (possibly accidentally) removed a link to JStor when editing one reference. Those links are very helpful for people at universities, since they can usually access JStor at no personal cost. So our general practice is to include the links if we have them at hand when we write the reference.

If you have any questions or issues, please feel free to contact me at User talk:CBM. — Carl (CBM · talk) 13:52, 20 March 2008 (UTC)

Ancestral relation

Hi! I had to undo one of your edits of the article Ancestral relation. Specifically, the edit made at 01:57, 23 February 2008‎. Before that, the formula for R* was correct:

$\mathbf {76:} \ \vdash aR^{*}b\leftrightarrow \forall F[\forall x(aRx\to Fx)\land \forall x\forall y(Fx\land xRy\to Fy)\to Fb]$

but after the edit it turned into the wrong formula:

$\mathbf {76:} \ \vdash aR^{*}b\leftrightarrow \forall F\forall x\forall y[((aRx\to Fx)\land (Fx\land xRy\to Fy))\to Fb]$

Please note that if you move quantifiers $\forall$ from the premise of an implication to outside the parenthesis, they should change to $\exists$. Please consult the standard textbook on mathematical logic for this.

Additionally, I added a (simple) proof that the Ancestral relation is exactly what is known as the transitive closure $R^{+}$ of a relation $R$. See Boolos's book "Logic, Logic, and Logic", page 8.

Finally, do you know who suggested the notation $R^{*}$? In view of the above, it is reasonable to replace it with $R^{+}$. (But carefully, in my proof of $R^{*}=R^{+}$). Thank you!

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