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nin



Joined: May 27, 2005

Post   Posted: Oct 05, 2011 - 00:16 Reply with quote Back to top

Well, given the answers, I'd like to point out that what you get in any machine is not real numbers but a limited subset of rationals and that explains why sometimes a machine may treat 0.9... and 1 as different.

Last round 3 coaches, so in for another show about that 1=0.9...

Supose they are not, and you get 1-0.9...=x with x>0
There must be a number of the form 0.0...01<x with n the number of 0s from the point to that poor lonely 1
1-0.9...9=y with n+1 9s is y>x but its exact value is the above mentioned 0.0...01<x argh!

So 1-0.9...=0 and 1=0.9...
uuni



Joined: Mar 12, 2010

Post   Posted: Oct 05, 2011 - 00:18 Reply with quote Back to top

As a related note, XKCD had something nice while ago: http://xkcd.com/356/
Gamer-man



Joined: Feb 12, 2004

Post   Posted: Oct 05, 2011 - 00:19 Reply with quote Back to top

.9 repeating - 1 would give you -.0repeating which is exactly 0 (it doesn't make sense to say an infinate series of 0's with a 1 at the end, as there is no end, it is just an infinate series of 0's, which is equal to 0)
Synn



Joined: Dec 13, 2004

Post   Posted: Oct 05, 2011 - 00:42 Reply with quote Back to top

Brother-Fu wrote:
Damn Paul, you really know how to give the nerds a hard-on...


He can also help solve what to do with it Very Happy

__Synn
**Seriously Pauly... stay off Crack(ed)
Cevap



Joined: Jun 24, 2009

Post   Posted: Oct 05, 2011 - 00:52 Reply with quote Back to top

Shraaaag wrote:
This reminds me of Zeno's paradoxes:
Pasted from wikipedia (cause I'm too lazy to write it myself):
Quote:
In the paradox of Achilles and the Tortoise, Achilles is in a footrace with the tortoise. Achilles allows the tortoise a head start of 100 metres, for example. If we suppose that each racer starts running at some constant speed (one very fast and one very slow), then after some finite time, Achilles will have run 100 metres, bringing him to the tortoise's starting point. During this time, the tortoise has run a much shorter distance, say, 10 metres. It will then take Achilles some further time to run that distance, by which time the tortoise will have advanced farther; and then more time still to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Therefore, because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise

We studied that in my class the other day, and we thought that the teacher was nuts! Razz
Sutherlands wrote:
DukeTyrion wrote:
Sutherlands wrote:
DukeTyrion wrote:
The problem is, the decimal system can never quite be exact.
Give me a fraction that can't be represented as a decimal, please.


Pi
Seriously? You think Pi is a fraction?

Isn't Pi actually a circle's circumference(I'm not sure this is the word I was looking for, feel free to correct me) divided by its diameter? That is a fraction in its own right, isn't it?
Sutherlands



Joined: Aug 01, 2009

Post   Posted: Oct 05, 2011 - 00:56 Reply with quote Back to top

Cevap wrote:

Isn't Pi actually a circle's circumference(I'm not sure this is the word I was looking for, feel free to correct me) divided by its diameter? That is a fraction in its own right, isn't it?
It's a ratio, not a fraction. Pi cannot be expressed as a fraction (with real numbers as both the denominator and numerator).
http://en.wikipedia.org/wiki/Pi
Cevap



Joined: Jun 24, 2009

Post   Posted: Oct 05, 2011 - 01:08 Reply with quote Back to top

Point taken, thanks for clarifying that one up, silly mistake when I think about it... But then again it IS 1 AM Razz
Fela



Joined: Dec 27, 2004

Post   Posted: Oct 05, 2011 - 01:38 Reply with quote Back to top

Sutherlands wrote:
Cevap wrote:

Isn't Pi actually a circle's circumference(I'm not sure this is the word I was looking for, feel free to correct me) divided by its diameter? That is a fraction in its own right, isn't it?
It's a ratio, not a fraction. Pi cannot be expressed as a fraction (with real numbers as both the denominator and numerator).
http://en.wikipedia.org/wiki/Pi


PI is not a rational number, it cannot be expressed as a fraction of rational numbers.

Of course it can be expressed as a fraction of REAL numbers, since it is also a real number. The easiest such expression is pi/1.

Pls don't confuse rational and real Smile.
PainState



Joined: Apr 04, 2007

Post   Posted: Oct 05, 2011 - 02:24 Reply with quote Back to top

in the same vein is this math issue that has allways perplexed me since 8th grade.

I was allways taught that between two points is infinite amount of numbers.

IE: between 0 and 1.

How can there be infinite amount of numbers/space between two points that are defined?

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Irgy



Joined: Feb 21, 2007

Post   Posted: Oct 05, 2011 - 02:33 Reply with quote Back to top

If you want to answer the question properly, you first need to accept that it's a matter of definition, not opinion nor intuition. Mathematics is ultimately just a model, defined by certain assumptions (called axioms), enhanced by more complicated defined terms, and supported by proven theorems. And there's a choice as to what those axioms and definitions are. There are actually mathematical models out there which deal with what's called "infinitessimal" numbers, which are intuitively values a bit like the difference between 0.999... and 1:
http://en.wikipedia.org/wiki/Infinitesimal

However, while interesting, infinitessimals aren't generally of much use to anyone. In "standard" mathemetics, which you are always assumed to be using unless you specifically state otherwise, infinitessimals are not part of the number system. The two values are defined to be flat out the same, interchangable, identical. No small difference, no close enough, the same.

If you want to answer the question, you really need to know the definition of an infinite decimal in the first place:
http://en.wikipedia.org/wiki/Decimal_representation

The value of an infinite decimal such as 0.999... is defined as the limit of the series "9/10 + 9/100 + 9/1000 + ...". So what is a "limit"? A limit of a series is not defined as a number that you get by adding a lot of terms together. It's the number which you can get as close as you like to by adding enough terms. That's the definition of a limit - in (relatively) plain English a limit of a series is a number with the property that if you tell me how close you want to be I can always give you a number of terms that will get you that close. The beauty of the definition is that you never have to actually add infinitely many numbers together. You just need to always be able to add together enough of the terms to get as close as you need to be.

So, the limit of "9/10 + 9/100 + 9/1000 + ..." is exactly 1, by the definition of a limit, and 0.999... is equal to the limit of that series, i.e. to 1, by the definition of an infinite decimal.

This question comes up a lot, there's been epic arguments about it on many a forum. The main reasons for this are:
* People are not taught the actual definition of infinite decimals in school. They're told some vague thing about adding an infinite number of little bits together. The actual definition is rock solid, but what people are taught is vague and doesn't make sense if you think about it deeply enough, and hence this confusion.
* Most decimal expansions are unique. The only exception is specifically this case of a finite decimal (like 1) and a decimal with an infinite series of '9's. Because every other decimal is unique it's surprising that these numbers with two ways of being written exist.
* It involves infinity, something which people are notoriously bad at dealing with.
* There's all manner of bad arguments both for and against it. If you look at the definition, there's no question about it, but if you try and make an intuitive argument you just get into a world of confusion.
Irgy



Joined: Feb 21, 2007

Post   Posted: Oct 05, 2011 - 02:38 Reply with quote Back to top

Oh and since I'm already linking to Wikipedia a lot:
http://en.wikipedia.org/wiki/0.999...
shadow46x2



Joined: Nov 22, 2003

Post   Posted: Oct 05, 2011 - 04:01
FUMBBL Staff
Reply with quote Back to top

as lulzy as math posts are...keep it to the correct forum :-p

you should know better paulie :-p

--j

_________________
origami wrote:
There is no god but Nuffle, and Shadow is his prophet.

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James_Probert



Joined: Nov 25, 2007

Post   Posted: Oct 05, 2011 - 09:49 Reply with quote Back to top

Irgy wrote:
However, while interesting, infinitessimals aren't generally of much use to anyone.


Lies! I use infinitesimals all the time! Every time I calculate an integral/differential I'm using the principle of taking dx to the infinitesimal limit. Hence I can find the area under a point, and the gradient of a line at a specific point. And get valid answers to my problems.

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Corvidius



Joined: Feb 15, 2011

Post   Posted: Oct 05, 2011 - 14:52 Reply with quote Back to top

I'm not a Mathematical genius but the concept of Infinity boggles the brain because it can't really exist, we cant even properly conceptualise it.

I do find the maths conundrums interesting though. Smile
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