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Topic: I must find out.
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dragonman97
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posted February 05, 2008 22:55
quote:
Originally posted by The Famous Druid:
Of course, the really important mathematical question is...
... what do you get when you multiply six by nine?
That there sounds like a mighty Question to me...
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Ashitaka
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posted February 05, 2008 23:09
quote:
Originally posted by MacManKrisK:
My own proof that .999... = 1
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1/3 = .333...
.333... * 3 = .999...
1/3 * 3 = 1
therefore .999... = 1
There you go, mathematics is fundamentally flawed! ![[crazy]](graemlins/crazy.gif)
1/3 does not equal it's decimal representative 0.3333....
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Xanthine
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posted February 05, 2008 23:47
quote:
Originally posted by The Famous Druid:
Of course, the really important mathematical question is...
... what do you get when you multiply six by nine?
54.
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And it's one, two, three / On the wrong side of the lee / What were you meant for? / What were you meant for?
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The Famous Druid
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posted February 06, 2008 00:01
quote:
Originally posted by Xanthine:
quote:
Originally posted by The Famous Druid:
what do you get when you multiply six by nine?
54.
/me cleverly deduces that Xanthine doesn't have 13 fingers.
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GrumpySteen
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posted February 06, 2008 07:06
quote:
Originally posted by The Famous Druid:
quote:
Originally posted by Xanthine:
quote:
Originally posted by The Famous Druid:
what do you get when you multiply six by nine?
54.
/me cleverly deduces that Xanthine doesn't have 13 fingers.
Are you sure? Did you check for any extras floating in a jar of formaldehyde in the back of her closet?
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Mac D
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posted February 06, 2008 15:28
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DoctorWho
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posted February 07, 2008 12:00
This whole argument comes down to the difference between potential infinity and actual infinity.
Potential infinity refers to a set of numbers that gets closer and closer to, but never quite reaches, an infinite end.
For instance, the sequence of numbers
1, 2, 3, 4, ...
gets higher and higher, but it has no end; it never gets to infinity. Infinity is just an indication of a direction -- it's somewhere off in the distance. This kind of infinity is like chasing a rainbow because when you get to where you thought it was, you see it is still further in the distance.
Actual infinity, is an infinity that you actually reach; the process is already done.
For instance, let's put braces around that same sequence:
{1, 2, 3, 4, ...}
This notation indicates the set of all positive integers. This set contains an infinite amount of members by definition.
The same thing can be said of the real numbers between 0 and 1. The number 0.999... approaches 1 but never reaches 1 just as the integers approach infinity but never reach it. The same reason people confuse potential infinity with actual infinity is the same reason people confuse 0.999... as equal to 1.
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Sxeptomaniac
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posted February 07, 2008 12:57
quote:
Originally posted by Mac D:
Is it bad that I think "Zeno's doughnut" is a pretty good joke? ![[Geek]](graemlins/geek.gif)
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Red Five
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posted February 08, 2008 18:23
In the case of the fractions, where .333 * 3 != 1/3 * 3: The decimal equivalents of many fractions are not exact. The "thirds" are a prime example: 1/3 is approximately .333..., but not exactly. Likewise, 2/3 is approximately .666..., but not exactly. Therefore, .333 is indeed .999, but 1/3 * 3 is exactly 1. Again, this is because .333 is approximately 1/3, not exactly 1/3.
It can get a little strange with certain numbers in the denominator, such as 6 or 12. Both are even numbers, but both are also evenly divisible by 3 as well as 2, so sometimes the decimal equivalent to the X/6 or X/12 fraction is rational, and sometimes it's irrational. I would theorize that any denominator that is evenly divisible by 2 and any other even number will give rational decimal equivalents, except when the denominator can also be evenly divided by 3. Denominators that are divisible by 5 should be similar, again unless also divisible by 3.
If I thought about it some more, I could probably come up with specific examples and some kind of pattern, but it's Friday night, and I'm not a math doctor (although my uncle is).
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The Famous Druid
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posted February 13, 2008 19:42
quote:
Originally posted by Steen: (in another thread)
x = 0.999...
100x = 99.999...
100x - x = 99.9999 - 0.999...
100 = 99
100 - 99 = 99 - 99
1 = 0
Um, shouldn't that be...
100x - x = 99.9999... - 0.9999...
99x = 99
x = 1
Not that I believe 1 = 0.99999... , I'm just sayin'
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Ashitaka
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posted February 14, 2008 00:19
OK, I will agree that the sum of the series "0.9 + 0.09 + 0.009 -> infinity" is equal to 1, but I do not agree that "0.999..." is equal to one. There is a philisophical difference. Being that 0.999.. is a number and the sum of the series is integration of many numbers.
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"If they're not gonna make a distinction between Muslims and violent extremists, then why should I take the time to distinguish between decent, fearful white people and racists?"
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DoctorWho
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posted February 14, 2008 11:12
Well I am not going to try and convince anybody that 0.999...=1 (after all I didn't think so myself) but when someone who is a good friend that has a PhD in math tells me that it's so, I tend to believe him.
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Laughter is like changing a baby's diapers. It doesn't solve anything but it sure improves the situation. Leo F. Buscaglia
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Callipygous
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posted February 14, 2008 14:30
Another way of looking at this is
.999 recurring = 1 - 1/infinity
any finite number divided by infinity = 0
so .999 recurring = 1
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The Famous Druid
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posted February 14, 2008 15:07
quote:
Originally posted by Callipygous:
Another way of looking at this is
.999 recurring = 1 - 1/infinity
any finite number divided by infinity = 0
so .999 recurring = 1
Not quite that easy,
(in all the examples below, assume n is infinity)
if (1-1/n) == 1,
and (1 ^ n) == 1 for all values of n
then you'd expect
(1-1/n)^n
to be 1 also,
Turns out, it's more like 0.367879...
(for the mathematical purists, (1-1/n)^n = 1/e for 'infinite' n)
In summary: infinity is weird, 1/infinity doubly so.
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If you watch 'The History Of NASA' backwards, it's about a space agency that has no manned spaceflight capability, then does low-orbit flights, then lands on the Moon.
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DoctorWho
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posted February 14, 2008 15:38
Sorry had a brain lapse there for a minute.
Edit: Ok here is a website that explains why .999~ = 1 almost exactly the way Dr. Holmes explained it to me. Take it or leave it.
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Laughter is like changing a baby's diapers. It doesn't solve anything but it sure improves the situation. Leo F. Buscaglia
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TheMoMan
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posted February 14, 2008 16:29
__________________________- I am not haveing trouble with the infinate string of numbers but that parallel lines will meet. How can that be? Parallel lines are that, parallel, and if infinatity goes on foreever how do the parallel lines meet, would that not make them curves, of some radius?
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sconzey
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posted February 15, 2008 08:10
That parallel lines don't meet is one of the axioms of Euclidean geometry.
My maths teacher once told me there was a non-euclidean geometry where they do.
What kind of geometry "actual" space obeys is still a matter of debate as far as I know.
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Richard Wolf VI
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posted February 15, 2008 08:36
In S2, the sphere's surface, parallel lines meet, for example.
Of course, as it already has been said, this corresponds to a non-euclidian geometry.
Another analogous example are meridians on the earth surface.
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maximile
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posted February 15, 2008 11:01
The Wikipedia page, the FAQs and discussion on its talk page and some of the posts here leave me in little doubt that "0.999… represents the same number as the symbol 1". And that 0.333... = 1/3 and 0.111... = 1/9 and so on.
I don't think there's any room for a "philosophical difference" between two equal numbers in mathematics, but a few years ago I didn't think that there was room for imaginary numbers so I can imagine that I'm missing something there. That said, nothing I've read seems to suggest such a difference.
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TheMoMan
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posted February 17, 2008 06:28
________________________ I am going to quote Sconzey here.
That parallel lines don't meet is one of the axioms of Euclidean geometry.
My maths teacher once told me there was a non-euclidean geometry where they do.
What kind of geometry "actual" space obeys is still a matter of debate as far as I know.
Okay lets say that they don't meet but are part of a real long slow helix, viewed from afar it would appear that they met or crossed but would continue until the next infinite loop. or twist.
So would these two crossing points be the start and stop of infinity?
Also what about those little buggers tacheons they go so fast that if you saw one "that it disappeared before you saw it" WTF was that? It must have been going the other direction from what it appeared to be going.
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If it don't glow it ain't Ham Radio
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Xanthine
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posted February 17, 2008 10:24
quote:
Originally posted by iWanToUseaMac:
In S2, the sphere's surface, parallel lines meet, for example.
Of course, as it already has been said, this corresponds to a non-euclidian geometry.
Another analogous example are meridians on the earth surface.
Why do the longitude lines meet but not the latitude?
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And it's one, two, three / On the wrong side of the lee / What were you meant for? / What were you meant for?
- The Decemberists
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TheMoMan
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posted February 17, 2008 12:50
___________________________ Lons. Pass through the poles. Whereas Lats. are Parallel to the equator.
If you go for a country drive in some states going N/S every few miles there will be a jog in the road, this is so that the surveyors can correct for proporty lines being parallel and the roads going N/S not being so.
The fun part is the sperical geometry trick. Start N at the equator go the the North Pole turn Left 90deg. go South to the equator, turn left again and go to the begining. Three ninety degree angles in one triangle.
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If it don't glow it ain't Ham Radio
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Serenak
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posted February 17, 2008 16:22
as you rightly say Mo Man, it is a trick... a trick of the sphere..
90 degrees (flat ortho) turned at each point... but it is not a flat ortho shape being drawn (as I know /you/ know far to well... I have no doubt your skill at 3 dimensional trig/geometry far outweighs mine - but the gag (like the scholar's mate) still stands true
On the original point - .9 recurring is not 1 nor will it ever be in maths... in real life if you get enough 999s it is "close enough" as per the earlier "mathematician & engineer & woman" example
In maths parallel line never meet, well not in "normal" geometry anyway. Mo Man's helix with a radius of infinity has potential - but in the maths I learned even that only allows for the "appearance" of covergence - like the sun appearing to go below the sea as it sets - then again infinity (like it's odd cousin root -1 (i) has some very strange and often mindbending properties... and if you think about them too hard you would find yourself with nasty factors like inf^inf or inf^i, etc...... ![[Eek!]](eek.gif) ![[Roll Eyes]](rolleyes.gif) ![[Beard of Peter Gabriel!]](graemlins/beardofpetergabriel.gif)
BTW and FWIW only a statistician can put his head in the oven and feet in the freezer and be "OK on average" ![[Big Grin]](biggrin.gif)
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maximile
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posted February 18, 2008 02:40
quote:
Originally posted by Serenak:
On the original point - .9 recurring is not 1 nor will it ever be in maths... in real life if you get enough 999s it is "close enough" as per the earlier "mathematician & engineer & woman" example
This has nothing much to do with "close enough". In maths, 0.999... is equal to 1. It's two ways to write the same number.
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TheMoMan
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posted February 18, 2008 03:31
______________________________ Maximile
This has nothing much to do with "close enough". In maths, 0.999... is equal to 1. It's two ways to write the same number.
I don't think so.
Now lets talk about the average weather. So you take all of the stats for one period of time and declare that that is what it supposed to be for this period of time. How does that happen, all that happens is more stats. for the average.
IF .9999 equals 1 then you must work at the reulators of banks office.
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If it don't glow it ain't Ham Radio
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