| Kytiara said: The wiki page just re-inforces what I meant at the very end of my last post. The answer is much more complicated than just saying 0.999... = 1, the key being the concept of limits |
Kind of true.
1) 0.999... is a notation. It, by definition, MEANS there's an infinite number of "9"s after the decimal point.
2) Once you accept that, 0.999... = 1. There is a gazillion proofs out there, the wiki page has a good collection of them.
On the concept of "infinity": it is by no means an intuitive concept. The ancient Greeks for instance could not come to grips with it--Zeno's paradox, for instance.
As to 0.999... : If you know "real analysis", or "analysis" for short, you'd know the history of it. It took a few centuries and some very brilliant mathematicians to lay out the foundations! It shouldn't be a surprise that without formal training people would be arguing over it over and over and over ...
P.S. Amount of "formal training": for the typical math student, he/she gets some exposure to real analysis in high school calculus. In college, typically there are 4 semesters of calculus (AP Calculus BC can place you out of the first 2 semesters typically, but it depends on the curriculum). A solid Real analysis is typically a junior/senior level course (2 semesters), a core requisite for math majors. However, most PhD level physical scientists and engineers are highly recommended to have a solid understanding of it.
the Wii is an epidemic.
