User talk:Bill Shillito

Welcome!

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DM Ashura
It is generally a faux pas to edit an article that is truly about oneself. Jimbo was told off when he did it to his own article, and it would be best if you stayed away from it for a little while.— Řÿūłóñģ ( 竜龍 ) 09:54, 4 December 2006 (UTC)

Under Alumni Association rules, you're considered an alumnus as long as you've completed a semester in good standing. There's no separate category for "current students" for that reason. —Disavian (talk/contribs) 04:18, 6 April 2007 (UTC)

Foot rating (Dance Dance Revolution)
Hey. Noticed you added a section on unrated songs. However, DDR:UK's simfiles - which generally seem to avoid coming up with foot ratings where they aren't available - give foot ratings of 3:5:9/3:5:9 for Flash In The Night (for example). Did they make this up, or did these numbers come from somewhere? Zetawoof(&zeta;) 20:30, 21 January 2007 (UTC)

Darboux function
Your edit in Darboux's theorem Special:Diff/810026267 was wrong and I've undid it.

The function given as an example
 * $$f:x \mapsto \begin{cases}x^2\sin(1/x) & \text{for } x\ne 0, \\ 0 &\text{for } x=0. \end{cases}$$

actually is Darboux, and one doesn't have to 'consider it to find a Darboux function'.

What concerns the derivative, which you mentioned in the edit description, we don't consider the $$f$$ function there, but rather
 * $$g:x \mapsto x^2\sin(1/x)$$

That function is defined on $$\mathbb R\setminus\{0\}$$, and its derivative $$g'$$ has the same domain; and the derivative is continuous at every point of its domain, hence it is continuous.

What concerns the former function, it is not differentiable at zero, so the domain of $$f'$$ is $$\mathbb R\setminus\{0\}$$ and it differs from $$\mathbb R$$, the domain of $$f$$. However, $$f'$$ is also continuous at every point of its domain, hence it is continuous, too.

--CiaPan (talk) 12:38, 13 November 2017 (UTC)


 * I'm very sorry, I didn't notice that someone modified the function in question (even though I have copied its definition above!) Now I have reverted both your recent change in a description and that unnecessary modification in the function's definition, so that the function is now defined, as previously, as
 * $$f:x \mapsto \begin{cases}\sin(1/x) & \text{for } x\ne 0, \\ 0 &\text{for } x=0. \end{cases}$$
 * Now it is, as the comment says, Darboux and continuous everywhere except the single point.
 * Best regards, CiaPan (talk) 09:05, 15 November 2017 (UTC)

Little error
Hello, I'm DVdm. Your recent edit to the page Division by zero appears to have added incorrect information, so it has been removed for now. If you believe the information was correct, please cite a reliable source or discuss your change on the article's talk page. If you would like to experiment, please use the sandbox. If you think I made a mistake, or if you have any questions, you can leave me a message on my talk page. Thank you. - DVdm (talk) 14:33, 23 October 2018 (UTC)