MathJoy

Media Downloader can help you download the PLAYING video or audio from Coursera and many other sites. Note when the  multimedia file is not in playing, Media Downloader cannot download it for you :) Download the extension and the tutorial from Google drive： https://drive.google.com/file/d/0B0yEgmz6VGdzZzgtcF8yZGhPcmM/view Microsoft OneDrive： http://1drv.ms/1NhYzYE

http://math.stackexchange.com/questions/1086713/is-0-an-infinitesimal In dictionary , Infinitesimal means ‘an indefinitely small quantity; a value approaching zero’, but natural language is a bad reference for mathematical definitions; it’s 'optimized’ for quickly conveying meaning in 'natural’ settings, not for expressing things precisely. In the context of nonstandard analysis, 0 should certainly be infinitesimal. Even in the limit case, you write “as x→0 f(x)→a” and you intend this to hold in the case that f(x) is constant equal to a. Therefore you need 0 to be considered infinitesimal if you want f(x)→a to be a formalization of infinitesimals. Basically it ends up making more sense to exclude zero in the cases where it should be excluded, then to explicitly include it where it should be included. Stylistically speaking, “nonzero infinitesimal” is much less clunky than “infinitesimal or zero”.