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This is an old revision of this page, as edited by Huon (talk | contribs) at 22:43, 25 January 2006. The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

I think you merit a canned welcome! Ahem:

Welcome!

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

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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 have any questions, check out Misplaced Pages:Where to ask a question or ask me on my talk page. Again, welcome!  Melchoir 20:29, 8 December 2005 (UTC)

Hello all! Thanks, Melchoir, for the welcome. Up to now, I have just amused myself by contributing to the discussion about 0.999... and 1. It is rather surprising, but even though imho the opponents of 0.999...=1 lack mathematical training and rigor, making their contributions difficult to read, I still learn something. Most interesting are the social aspects:

- Practically all proponents of 0.999... have accounts and routinely sign their messages.

- To my knowledge, only one of the opponents had an account, and many don't even sign their messages.

- Almost all who have formal mathematical training (including at least one MIT lecturer) agree that equality holds,

- while the opponents make claims like "No mathematician who *knows* what he is talking about will agree with you.", but seem to be at a loss to present just one example of such a "mathematician who *knows* what he is talking about" (there was a link to a constructionist who made up a new system of numbers called "decimal numbers" as opposed to the usual "real numbers"; interesting reading, once more, but he does not state anything about the relation of the real number represented by 0.999... to 1).

Probably it would be better not to feed the trolls, but I rather think that ignoring them would be seen as "capitulation of the PhDs", and I am not exausted yet... ;-) Have fun! --Huon 11:13, 9 December 2005 (UTC)

Okay, by now the 0.999...=1 discussion boiled down to divergent views about what 0.999... should be, and the mathematical community's view that it is ${\displaystyle \lim _{n\to \infty }(\sum _{i=1}^{n}{\frac {9}{10^{i}}})}$ (and thus equal to 1) seems to have prevailed. Probably I'll have to look at something else in the future. --Huon 12:15, 11 December 2005 (UTC)

Word. (I have nothing insightful to add.) Melchoir 03:40, 14 December 2005 (UTC)

Analysis

The 0.999...=1 discussion once more seems to be alive and well. This time, anon decided to launch a frontal assault on all of analysis: It is "full of errors and contradictions", even professors with 30 years of experience teaching analysis "are still unable to demonstrate flawless proofs", students don't grasp what it's all about and forget it again as soon as possible. I cannot let that stand unchallenged, but it would be quite off-topic on the proof talk page.

I don't know those professors; thus, I cannot discuss their abilities. Of course everybody makes mistakes, including professors, but that does not mean that flawless proofs are not available. And if those professors are indeed unable to demonstrate flawless proofs, I'm not surprised their students don't understand them.

It is rather easy to make an analysis lecture extremely abstract very quickly. Then most students will indeed face severe problems, especially since analysis is usually one of the first lectures and students are only used to the rather low level of abstraction taught at school. But that is a question of didactics, not mathematics.

Concerning the errors and contradictions: It is easy to make such a general claim. Name just one of these errors and contradictions, and we can discuss it in detail! --Huon 22:43, 25 January 2006 (UTC)