.9999 = 1?

[boomboom]

http://en.wikipedia.org/wiki/0.999...

todays feature article.

[Jeff Olsen]

Another take on the subject (http://www.straightdope.com/columns/030711.html) (note #56 in the Wiki article).

[ohms_law]

Q: Why are we talking about this incredibly esoteric topic when there are so many more interesting things to discuss, like whether Rebecca Romijn-Stamos is wearing anything besides blue body paint in the new X-Men movie?

A: Because it's cool, you wanker. Here, have a banana while the rest of us discuss.
bwahahahaha!

[SFSteveG]

I've been out of math for too long.

[boomboom]

my thought....on this...

1/3=.3333~
2/3=.6666~

1/3+2/3= 3/3= 1

but: .33333~+.66666~= .999999~

does not equal one. It is almost equal to the whole. But not quite. Even on a billionth decimal point...still not equal....

but get this, if you minus 1.000~ from .99999~ = 0.000~

interesting stuff :)

[ohms_law]

if 1/3 + 2/3 = 1, then .333~ + .666~ must equil 1.

how do you justify having two different results simply because your notation changes?

If you ask me, there really isn't such a thing as an exact third of something. one peice is always going to be infantesimmaly larger than the rest, and therefore will not be 1/3 (.333~).

[boomboom]

heres a thought,
you already know this
maybe 1/3+2/3= 3/3

but maybe
3/3<1

[SFSteveG]

heres a thought,
you already know this
maybe 1/3+2/3= 3/3

but maybe
3/3<1

nope. The point is that 1/3 is a literal third so that .333...=1/3. It's a "close enough" issue.

[ohms_law]

right.

This actually works out in reality as well. take a peice of paper and try to cut it into exactly three peices. you'll eventually with practice be able to get close enough so that the sizes of the peices are visibly identical, but if you measured them one would always be slightly larger. but, there "close enough" that the eye cannot distinguish the difference.

[FRENCHREDSOX]

Decimals are perfect only when the total is surmizable in quantum logic


Wheras fractions ARE perfect splits

[FRENCHREDSOX]

Thus 1/3 is (approx) equal to .333 recurring but 1/3 does not = 0.333~ as
~ is undefinable as yet


"Even as the finite encloses an infinite series
And in the unlimited limits appear,
So the soul of immensity dwells in minuta
And in the narrowest limits, no limits inhere
What joy to discern the minute in infinity!
The vast to perceive in the small, what Divinity!"

– Jakob Bernoulli

[ohms_law]

Fractions are not "perfect splits"...
1 divided by 3 = .333~
1 divided by 2 = .5
it's just the way that math works is all. In reality, everything is (aparently) finite. therefore, there is no physical way to actually acheve the mathimatical perfection of an infinite repeating number. at some point in the measurement, something stops the value that is being measured.

You can say that there's no such thing as two perfect halves of something in the same way that I said that there's no such thing as three perfect thirds.
Reality can be described in math, but the physical limits of reality defy the perfection of math.

[FRENCHREDSOX]

Fractions are not "perfect splits"...
1 divided by 3 = .333~
1 divided by 2 = .5
it's just the way that math works is all. In reality, everything is (aparently) finite. therefore, there is no physical way to actually acheve the mathimatical perfection of an infinite repeating number. at some point in the measurement, something stops the value that is being measured.

You can say that there's no such thing as two perfect halves of something in the same way that I said that there's no such thing as three perfect thirds.
Reality can be described in math, but the physical limits of reality defy the perfection of math.

Um you are incorrect - fractions actually are perfect "splits" it is there conversion to decimal fractions which are incorrect .The basis of mathematics involving infinite is:
Accuracy is a measure of rightness. Precision is a measure of exactness.

This can be shown in the following example
e = Accuracy Precision
27 NO NO
2.18281828 NO YES
2.72 YES within 1 ppk NO
2.718281828 YES YES

Also the works of Axler shows that at the 23rd level of decimal fractions there
is no certitude that the accuracy is correct & possibly quantum mathematics should be applied.
http://www.phy6.org/outreach/edu/contfrac.htm
http://www.inwap.com/pdp10/hbaker/hakmem/cf.html


Also Feydman in his work states that recurring decimal binary fractions have a inconsistence at -37th level (he uses Einstein theort & the work of Schlessinger as a basis)

Quantum maths use FRACTIONS because of their precision & accuracy as do standard mathematical formulae because of
this fact thus 1/3 + 2/3 = 1

as you can see here this is not the case for binary decimal fractions due to the instability of decimals at lower case levels
http://members.cox.net/srice1/profdeley/math/infinity.html

By numbers, I mean all possible fractions that lie between zero and one as well as all possible decimals (that aren’t fractions) that lie between zero and one. The following is similar to the proof
http://tutorial.math.lamar.edu/AllBrowsers/2413/TypesOfInfinity.asp

[disposablehero]

so, did we just find out what FRS does for a living?

[ohms_law]

Um you are incorrect - fractions actually are perfect "splits" it is there conversion to decimal fractions which are incorrect .The basis of mathematics involving infinite is:
Accuracy is a measure of rightness. Precision is a measure of exactness.
etc...

uh huh.
give me a micrometer that can measure to the quadrillianth decimal place...

[FRENCHREDSOX]

uh huh.
give me a micrometer that can measure to the quadrillianth decimal place...

There you again... DECIMALS which are not "perfect" but fraction are (ie 1/7 or 1/3) & leading to that are inacurrate...

easy one here : (1/3 + 2/3) = (.333 + .666)
right then E(1/3 + 2/3) = E (.333 + .666)
but if E is expotentially large the formulae is incorrect


it should be (1/3 + 2/3) = ~(~.333 + ~.666):)

[FRENCHREDSOX]

uh huh.
give me a micrometer


It's micrometre....(& that only measure to power -6) you should be talking abou nanos (& even then they are too large)...





that can measure to the quadrillianth decimal place...

as yet upto -8 we can "see" - post -8 there has to be either a comp sim (imprecise) or the usage of fractions & a "tendency" towards Quantum maths but a better mathematician/physician than I would be able to develop that even at the "Quadrillienth" dp there is no tendency to convergence & that a resulting multiplication by the same positive factor would lead to divergence

[ohms_law]

as yet upto -8 we can "see" - post -8 there has to be either a comp sim (imprecise) or the usage of fractions & a "tendency" towards Quantum maths but a better mathematician/physician than I would be able to develop that even at the "Quadrillienth" dp there is no tendency to convergence & that a resulting multiplication by the same positive factor would lead to divergence

Exactly my point. Thank you.

ps.: thanks for the spelling lession. my world is complete now.

[FRENCHREDSOX]

Exactly my point. Thank you.

What !!! "Seeing is believing" - if you use that analysis then the world is flat

[FRENCHREDSOX]

Fractions are perfect every time & binary decimal fractions are not always

[ohms_law]

What !!! "Seeing is believing" - if you use that analysis then the world is flat


Fractions are perfect every time & binary decimal fractions are not always

No, I don't think the world is flat. geez.
You can't measure something to an infinite accuracy. It's not physically possible. Therefore, in the real world, there is no such thing as a "perfect" fraction. There cannot be, since anything used to measure something will by definition be rounding that measurement at some point.
If we're talking about math in the purely abstract sense then sure, 1 divided by 3 equils .333~, and that repeating fraction never ever ends.

The whole point of saying that .333~ + .333~ + .333~ = 1 (and not .999~) is that in the real world, there are no infinite objects. There's always that one grain of sand, one molecule, one atom, one electron, one quark, one something that ends up causing one side or the other to be "larger".

[FRENCHREDSOX]

thats not what mathemiticians nor physicians would say - 1/3 is perfect,as are all fraction which have not been converted into metric analysis

[ohms_law]

luckily, mathematicians and physicists don't actually build things. engineers do.
;)

[SFSteveG]

so, did we just find out what FRS does for a living?

I hope so.

[SirKodiak]

luckily, mathematicians and physicists don't actually build things. engineers do.
;)

Heh, in most fields, the engineers use the work of the scientists to make plans for mechanics, laborers, craftsmen, etc to actully make something. I always have seen the engineer as the translator between the physicist and mechanic. I was in engineering for 2.5 years of college, and that experience, along with my experience with engineers at a refinery, makes me think most engineers are closer to the scientist than the mechanics.

[ohms_law]

no arguments from me there. The difference is that an engineer mostly deals in what's possible, whereas theoriticians deal mostly with what's probable. This discussion is a great example of that.
:)

[SirKodiak]

It's micrometre....(& that only measure to power -6) you should be talking abou nanos (& even then they are too large)...


I do believe he is talking about the measuring tool called a micrometer, not the actual distance of measure micrometer, and the accuracy of a mic is dependant upon how the device is made.

[ohms_law]

yup, you got it.

the real point to me saying that though is that, no matter how accurate the device is, that accuracy means that a decimal is being rounded at some point. Therefore, it is not possible to measure to an infinite level of measurements. and therefore, there is no such thing as a true .333~, because obviously the string of three's ends somewhere (weather that decimal place is far enough to the right to make it a moot point is another subject).

[FRENCHREDSOX]

luckily, mathematicians and physicists don't actually build things. engineers do.
;)

Engineers/architects/modelers thankfully USE Mathematicians & physicists theorems as their basis for their work (from simple laws such as gravity all the way to stress related theorems based on calculated development of global temperature changes etc):rolleyes:

[FRENCHREDSOX]

yup, you got it.

the real point to me saying that though is that, no matter how accurate the device is, that accuracy means that a decimal is being rounded at some point. Therefore, it is not possible to measure to an infinite level of measurements. and therefore, there is no such thing as a true .333~, because obviously the string of three's ends somewhere (weather that decimal place is far enough to the right to make it a moot point is another subject).

its due to "moot" points that devlopments occur - quantum physics lead to realtivety theorem.Q-maths the developments space size & "black hole" understanding.

If you accept that ~.333 is finite then 80% of modern physics & mathematic theorems are no longer valid

[ohms_law]

I never argued that. I simply stated that in the real world, where Newtonian physics laws apply (like here on earth, not in and around black holes) there are no infinite fractions. You can take a ruler, some calipers, a micrometer, or any measuring device and actually measure from one point to another.

Anywhere in the universe that you can apply an infinite number in measuring something, you get really strange things going on such as black holes. How do you measure the weight of a black hole? the size of the universe? the age of the universe? etc... you can't use a really big measuring stick or set of scales.

ps.: relativity lead to quantum physics.
;)

[FRENCHREDSOX]

I never argued that. I simply stated that in the real world, where Newtonian physics laws apply (like here on earth, not in and around black holes)
That is the point LAWS in physics,maths etc are LAWS you cannot chop n change & choose which apply where....same Gravity laws apply on Earth or around ablack hole & infinity applies here & around a black hole

http://www.iop.org/EJ/abstract/0264-9381/14/8/023



there are no infinite fractions. You can take a ruler, some calipers, a micrometer, or any measuring device and actually measure from one point to another.

Yep you just contradicted yourself - & said what I have been saying all along FRACTIONS are finite & DECIMALS can be finite & infinite - thus creating your supposed paradox of " ~+~= a figure"


Anywhere in the universe that you can apply an infinite number in measuring something, you get really strange things going on such as black holes. How do you measure the weight of a black hole? the size of the universe? the age of the universe? etc... you can't use a really big measuring stick or set of scales.

ps.: relativity lead to quantum physics.
;)

They are not strange at all - interesting yes,unusual yes - but all apply & respect laws of mathematics & physics

[FRENCHREDSOX]

Read Katz's "zero_infinity" lectures,Feydham or even Hawkins .... they use fractions because they are the ONLY finite variable which allows standardisation of "natural laws" to be extrapolated into a "substantial" equilibrium to create a defined "theorem" of Quantics

http://www.hawking.org.uk/text/public/warps.html his other works can be found on his site at Cambridge

[ohms_law]

yes, yes, yes. You're being stubborn. There are rules that apply to some situations, and not others. That's what started Quantum physics to begin with, is Einstein and other's trying to develop a "Universal theory of everything". There simply are no laws that describe every possible situation in the universe.

yet.

[FRENCHREDSOX]

Nope Quantum works everywhere & was developed because "rational" physics/maths DIDN'T work at the infinite tendency levels (small or big) .

QM & QP could be applied & taught in school or even at SAT level but would require a complete re-vamp of the classes & basically would throw out all the other classes just for students to get to grips with the basics

But anyway I m stopping here....

[ohms_law]

Quantum works everywhere
what do you base that statement on? everything that i've been taught about Quantum Mechanics and Quantum Physics makes it a point to state that Quantum rules do not apply everywhere, equaly.