User talk:Hodge Star

Welcome!

Hello, Hodge Star, and welcome to Wikipedia! Thank you for your contributions. I hope you like the place and decide to stay. Here are a few good links for newcomers:

I hope you enjoy editing here and being a Wikipedian! Please sign your name on talk pages using four tildes (~~~~); this will automatically produce your name and the date. If you need help, check out Wikipedia:Where to ask a question, ask me on my talk page, or place {{helpme}} on your talk page and someone will show up shortly to answer your questions. Again, welcome! Oleg Alexandrov (talk) 05:26, 24 February 2006 (UTC)[reply]

Cauchy sequence[edit]

I reverted your edits at Cauchy sequence, as you inserted the absolute value where it was supposed to talk about a metric space, which has a distance. If you would like to make that article more elementary, I would suggest you insert the definition using the absolute value in the section about real numbers, below the section about metric spaces.

And one suggestion, it is good if you use an edit summary. It explains what your intention is, when changing something. Thanks. :) Oleg Alexandrov (talk) 02:05, 24 February 2006 (UTC)[reply]

In reply to your post to my page regarding my Cauchy sequence edit, first, thank you for the post and letting me know about the "edit comments" things. However, regarding the subject, I still feel it correct.

The definition of a Cauchy sequence involving the absolute values doesn't just apply to real numbers; it also applies to rational numbers and integers. It implies to any Cauchy set. It is also the definition given in any introductory Real Analysis textbook. While it certainly may not belong under any "metrix spaces" section, I still feel that it is the fundamental definition of a Cauchy sequence, and one that people are likely to look for. It merely puts the statement I edited into some more mathematical and intuitive language.

Still, I won't edit it back without discussing it with you first, first and foremost since I'm so new to this whole "wikipedia" thing.

Thanks! —The preceding unsigned comment was added by Hodge Star (talk • contribs) .

Yeah, that's what I said, it was not in the right section. I had more time now, so I integrated your remark. You are right, it is good to start with the reals first, and go to metric spaces later. Cheers, Oleg Alexandrov (talk) 05:23, 24 February 2006 (UTC)[reply]

Oleg is right: in most metric spaces there is no such thing as absolute value of a point. Certainly with real, rational, complex, etc. numbers there is, and in many sorts of vector spaces there is, but not generally. Look at Principles of Mathematical Analysis by Walter Rudin. Michael Hardy 22:10, 24 February 2006 (UTC)[reply]

One more remark[edit]

When you insert a new section, there is no need to put capitals in the title; one capital is enough. I fixed that now at square root of 2. Welcome, and I hope you like it here! Oleg Alexandrov (talk) 05:26, 24 February 2006 (UTC)[reply]

Simpler "proof" that the square root of 2 is irrational[edit]

Your proposed proof is circuluar; it proves nothing at all. You say b√2 should be an integer, "but it isn't". That last phrase, "but it isn't", is just what you need to prove! You haven't done that; you've merely asserted it. Michael Hardy 22:15, 24 February 2006 (UTC)[reply]

thanks[edit]

Thank you both for your feedback. Guess I do need to be more careful about how explicit I am in everything before I go and post. Glad the community here is patient with its newbies! -Hodge Star