Website review: 0.999... - Wikipedia, the free ency...
jorganizam discovered this in Mathematics
•14 reviews since Oct 27, 2006
mathematics
•en.wikipedia.org/wiki/0.999
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Reviews of this website
jorganizam discovered 21 months ago- From the page: "In mathematics, 0.999... is a recurring decimal exactly equal to 1. In other words, the symbols '0.999...' and '1' represent the same real number. *** The equality has long been taught in textbooks, and in the last few decades, researchers of mathematics education have studied the reception of this equation among students, who often reject the equality. The students' reasoning is often based on an expectation that infinitesimal quantities should exist, that arithmetic may be broken, an inability to understand limits or simply that 0.999... should have a last 9. These ideas are false with respect to the real numbers, which can be proven by explicitly constructing the reals from the rational numbers, and such constructions can also prove that 0.999... = 1 directly. At the same time, some of the intuitive phenomena can occur in other number systems. There are even systems in which an object that can reasonably be called "0.999..." is strictly less than 1. *** assertion: 3 × 0.333... = 0.999... assertion: 0.333... = 1⁄3 step 1: 3 × 0.333... = 3 × 1⁄3 proof: 0.999... = 1 "
- reckoness rated 7 months ago
- I need to look at this.
- Zigphroid rated 8 months ago
- An excellent article documenting a serious BUG in math and number systems. Or maybe its a bug in our brains comprehension of rather long numbers..
- Tru7h rated 20 months ago
- Gotta disagree with davethecave here. There are admittedly many sites out there that give simple equations to try and prove it, but this Wikipedia article fully explains it from a neutral point of view. Good read.
- Krytain rated 20 months ago
- @davethecave 1/3 DOES equal 0.333333..., and .99999... DOES equal 1. If you would actually read the webpage or know anything of math, you would understand. While there is a proof that .99999... is less than 1, it is smaller my an infinitly small number, which would be considered 0.
- kb-ganesh rated 20 months ago
- I thought I knew maths..Now I am not so sure..
- Wikipedia is just awesome!
- I get too few *good* math links on stumble :-/
- Dowell rated 20 months ago
- From the page: "Students of mathematics often reject the equality of 0.999%u2026 and 1, for reasons ranging from their disparate appearance to deep misgivings over the limit concept and disagreements over the nature of infinitesimals. There are many common contributing factors to the confusion:"
- davethecave rated 20 months ago
- I am getting a little fed-up with sites trying to tell me that 0.999.. is the same as 1. The basic arguament is flawed, 1/3 does NOT equal 0.33333.. Its just an approximation. By the end of these essays, I am so bored with the so-called proofs, I pretend to accept the arguament and stumble forward to some pretty pics of butterflies or mountain vistas. Move on, the maths geeks are confused.
