2570 replies to this topic

[SpazCat]

2441: Wants to get a job working from home.

[Xteven Xavier]

2442: palindrome yay.

[Stars]

2443: A man, a plan, a canal, Panama.

[panda]

2444 refers Stars to the Archimedean property of real numbers

 

http://en.wikipedia....#Infinitesimals

 

 

Specifically, the difference 1 − 0.999... must be smaller than any positive rational number, so it must be an infinitesimal; but since the reals do not contain nonzero infinitesimals, the difference is therefore zero, and therefore the two values are the same.

[Stars]

2445 wonders if 2444 read that whole subsection and saw the counterpoints to 0.999...=1 a few paragraphs down.

[panda]

2446 has read the entire article and finds no such counterpoints (unless one reads something out of context or without understanding advanced concepts).

[Stars]

2447 did not read the whole article because this and the explanation for it did not even require scrolling to locate:

 

 

EDIT: And upon reading the introductory section:

 

Some alternative number systems, such as the hyperreals, do contain nonzero infinitesimals. In most such number systems, the standard interpretation of the expression 0.999... makes it equal to 1, but in some of these number systems, the symbol "0.999..." admits other interpretations that contain infinitely many 9s while falling infinitesimally short of 1.

[Xteven Xavier]

2448: so tired

[panda]

2449 The equation above represents hyperreal notation. It's the same way as expressing 0.999... in real notation. The point of the authors (Katz & Katz, Ely, and god-of-Calculus Ian Stewart) cited in that particular section of the Wikipedia article is that both standard and non-standard notations may not convey the idea to students leading to all this confusion. 0.999... is not properly defined in ANY number system. Rather, it represents an idea; that it is precisely the same as 1. This is true even in hyperreal notation. Both Stewart and Katz & Katz repeatedly state that 0.999... = 1. All this is to illustrate that the point of mathematics is ideas and discussion and concepts, even of things that seem absurd and may not exist. Everything leads back to philosophy.

[SpazCat]

2450: Can you two go make math love somewhere else? I refuse to even glance at math. 

[panda]

2451 I'm trying to make you as frustrated as possible so you'll have a cleaner house. I'm sure VP would appreciate my efforts.

[Xteven Xavier]

2452: boredom has set in, the world b is beginning to fluctuate with daydreams and it's beginning to be hard to distinguish fantasy from reality.

[Stars]

2453:

 

[Xteven Xavier]

2454: has been up all night and is bored

[Stars]

2455 recommends a Wheel of Time book. Those will keep you occupied for a loooong time.

[Xteven Xavier]

2456: really enjoys the wheel of time series, up thorough book 8 anyways, haven't read any more. But also don't have the money for books right now, or a computer to get then illegally.

[SpazCat]

2457: Has pawned the kids off to the babysitter and is loving the quiet house.

[Xteven Xavier]

2458: declares hooray for you.

[BottomGuy]

2489 is only posting to see if his Link avatar is working.

[Xteven Xavier]

2490: yay it works.