.9 repeating = 1? Is our numerical system flawed?

[atsimg]http://files.abovetopsecret.com/images/member/e77a6e6b5f0b.jpg[/atsimg]

reply to post by Smack


Let me get this right, you say my humorous post was off topic but leave all of the nonsensical garbage of one poster untouched? Pfft! Some mods have NO sense of humor or proportion.

Originally posted by Smack
reply to post by Smack

 

Let me get this right, you say my humorous post was off topic but leave all of the nonsensical garbage of one poster untouched? Pfft! Some mods have NO sense of humor or proportion.

some mods are willing to hear a fella out.

go here to see why we should NOT dis the ancients and the obvious clues left behind.

breakfornews.com...
breakfornews.com...

Maltese Cross is here to tease some of you.
Asymmetry is a river that runs through the entire creation.

Why dis it?

namaste

[edit on 14-3-2010 by CHiram_Abiff]

reply to post by CHiram_Abiff


What are you really saying?

PI does not really equal to 3.14159.....?
That 1 does not really equal to 0.999...?

Originally posted by Deaf Alien

What are you really saying?

PI does not really equal to 3.14159.....?

I thought that was clear by the 22/7 equation.
'rational pi ... not irrational pi in the sky'

somewhere between the twix, it is all in the mix
discrete vs. continuous?

Originally posted by Deaf Alien
That 1 does not really equal to 0.999...?

maybe?

did ya know that if 'c = 1'

then E=M in the equation E = Mc^2?

namaste

[edit on 14-3-2010 by CHiram_Abiff]

[edit on 14-3-2010 by CHiram_Abiff]

Click here for more information.

Originally posted by davesidious
reply to post by CHiram_Abiff

 

c does not equal 1, so you don't have a point.

This thread is discussing 0.9999999 = 1, not your whacky ideas about Pi or E=MC².

I realize what you were discussing...
why do YOU folks keep taking it elsewhere?

how about discussing my wacky ideas that got attacked long ago.
did you read that post?

go back and do.
till you do....your comments are IGNORANT...

out of context...
we were debating whether ancient beliefs and concepts vs. modern beliefs shared archetypal structure?

irrational pi = 3.141 vs rational pi = 22/7 became examples.

you fellas only went after the usual piece of pi?
why no 22/7 = pi ?

anyway the argument stands .... old wisdom needs to be remembered and dusted off.

clearly.
IMHO

you fellas have problems with humble opinions?

namaste

[edit on 14-3-2010 by CHiram_Abiff]

reply to post by CHiram_Abiff


Start a new thread for a different topic. That's how forums work. You have not even mentioned the OP recently. You are off-topic.

Originally posted by davesidious
You have not even mentioned the OP recently. You are off-topic.

clearly because I was being attacked
not one person was willing to discuss the original post.

hmm
interesting.
I see it differently.
I arrived
made one comment

the MOB gathered and attacked
go back and read it for yourself.

you are still at it?

namaste

[edit on 14-3-2010 by CHiram_Abiff]

Further Off Topic Posts will be removed. There has already been a warning (it really isn't too difficult to start a new thread).

Further Violations May Result In The Closing Of This Thread.

Originally posted by The Vagabond

And 1/3=.333

As far as I can tell, we can't have a perfect system of maths unless there is a "lowest number" which can not be divided, subtracted from, or inverted to a negative.

I was wondering if anybody else had any insight on the matter.

[edit on 24-3-2005 by The Vagabond]

divide '1' the loneliest number three times or THRICE times by '3'

1st step
1/3 = .3333333333333

2nd step
.33333333333/3 = .11111111111111

3rd step
.11111111111/3 = .037037037037037
So what is the significance of 37?
www.biblewheel.com...

Again the point I am trying to make....
You can NOT separate fact from fiction.

The fiction called the bible that is veiling NUMERICAL laws embedded in those bible narratives.

myth = math = music

re: they have a lowest and highest number.
the lowest is the planck length.
en.wikipedia.org...

So what is the largest?
Can both the lowest and highest can be expressed as 'octaves'?

namaste



[edit on 17-3-2010 by CHiram_Abiff]

[edit on 17-3-2010 by CHiram_Abiff]

reply to post by CHiram_Abiff


Kinda old thread, but the topic fits - check out my threads on my signature about PI - the pdf will show a closed form formula and is verifiable..

I didn't read through the whole thread, so perhaps someone actually got around to proving that 0.999... = 1 when working with real numbers. This is not a matter of belief, nor does it actually have to do with infinity as most people think of it. In actual mathematics, infinity is used as shorthand for states such as "for any arbitrary n>N some condition is met." To comprehend why in the world 0.999... = 1, first make sure you know what 0.999... means. 0.999... does not mean 0.9 followed by an arbitrarily large amount of 9's, nor does it mean 0.9 followed by an infinite number of 9's. To the first, 0.9 followed by any finite amount of 9's is certainly a number less than 1. To the second, see my comment above concerning infinity. When representing a number with decimal expansion, use the definition of decimal expansion! Decimal expansion denotes a number that is the limit of the sequence (a, a b/10, a + b/10 + c/100,...). For example, 2.25 is equal to the limit of (2, 2 + 2/10, 2 + 2/10 + 5/100, 2 + 2/10 + 5/100 + 0/1000, + 2 + 2/10 + 5/100 + 0/1,000 + 0/10,000). It is easy to see that the limit of this sequence is 2 + 2/10 + 5/100 = 9/4.

But what is a limit? Again, go by the standard mathematical definition! A limit of the sequence (x_n) is a number L such that for any number E>0 there exists an natural number N such that for any natural number K such that if K is greater to or equal than N, |L-(x_K)| < E. In English: The sequence (x_n) is arbitrarily close (that is, less than any E) to L at some point in the sequence (that is, at the Nth term) and every point thereafter (any Kth term after the Nth term). Furthermore, if a sequence has a limit, it is unique. There is no doubt that the sequence (0.9, 0.99, 0.999, 0.9999,...) can be arbitrarily close to 1 simply by reaching some term in its sequence. It is impossible to show that there is a number greater to or equal than 1 that can possibly equal 0.999… as the sequence would either surpass the number and begin diverging from it or there would be a fixed gap between the proposed number and the limit of the sequence (e.g., if you think 0.999… = 1.1, then you will never find a ϵ

a reply to: Soylent Green Is People

Traditional Pi 3.141592653589793 multiplied by 2 is traditional Tau 6.283185307179586.
Golden Pi 3.144605511029693 multiplied by 2 is Golden Tau 6.289211022059386.
Traditional Tau 6.283185307179586 says that if the circumference of a circle has 36000 equal units of measure then the radius of the circle is 5729.577951308232523 (reduced to 4 decimal places is 5729).
Alternatively traditional tau 6.283185307179586 says that if a circle has a circumference of 360 then the radius of the circle is 57.295779513082325 (reduced to 4 decimal places is 57.29)
Golden Tau 6.289211022059386 says that if the circumference of a circle has 36000 equal units of measure then the radius of the circle is 5724.088422813310602 (reduced to 4 decimal places is 5724).
Alternatively Golden Tau 6.289211022059386 says that if a circle has a circumference of 360 then the radius of the circle is 57.240884228133106 (reduced to 4 decimal places is 57.24)
It is a Geometrical fact that if one 8th of a circle’s circumference is multiplied by the square root of 1.618033988749895 (1.27201964951406) then the result is the measure for the radius of the circle. 1.27201964951406 is the ratio gained from dividing the second longest length of a Kepler scalene right triangle by the shortest edge length of the Kepler scalene triangle. If the radius of a circle is divided by one 8th of the circle’s circumference then the resulting ratio is the square root of 1.618033988749895 (1.27201964951406).
We can use the Pythagorean theorem to determine which value of Pi is correct out of Traditional Pi 3.141592653589793 or Golden Pi 3.144605511029693: en.wikipedia.org...
So if the circumference of the circle is 360 and one 8th of 360 is 45. So if the shortest edge length of a Kepler right triangle is 45 then according to the Golden ratio of Cosine (36) multiplied 2 = 1.618033988749895 the hypotenuse of the Kepler right triangle is 72.811529493745275. If the hypotenuse of a Kepler right triangle is divided by the shortest edge length of a Kepler right triangle then the result is the Golden ratio of Cosine (36) multiplied 2 = 1.618033988749895. 72.811529493745275 divided by the Golden ratio of Cosine (36) multiplied 2 = 1.618033988749895 is 45.
72.811529493745275 squared is 5301.518827218538062.
45 squared is 2025.
5301.518827218538062 subtract 2025 = 3276.518827218538062.
The square root of 3276.518827218538062 is 57.24088422813311. (reduced to 4 decimal places is 57.24).

So if the circumference of the circle is 36000 and one 8th of 36000 is 4500. So if the shortest edge length of a Kepler right triangle is 4500 then according to the Golden ratio of Cosine (36) multiplied 2 = 1.618033988749895 the hypotenuse of the Kepler right triangle is 7281.1529493745275. If the hypotenuse of a Kepler right triangle is divided by the shortest edge length of a Kepler right triangle then the result is the Golden ratio of Cosine (36) multiplied 2 = 1.618033988749895. 7281.1529493745275 divided by the Golden ratio of Cosine (36) multiplied 2 = 1.618033988749895 is 4500.
72.811529493745275 squared is 53015188.272185380623353.
4500 squared is 20250000.
53015188.272185380623353 subtract 20250000 = 32765188.272185380623353.
The square root of 32765188.272185380623353 is 5724.088422813311. (reduced to 4 decimal places is 5724).

a reply to: CHiram_Abiff

Alternative geometrical method for determining which Pi is the correct value of Pi 3.141592653589793 Traditional Pi or Golden Pi 3.144605511029693:

Traditional Pi 3.141592653589793 multiplied by 2 is traditional Tau 6.283185307179586.
Golden Pi 3.144605511029693 multiplied by 2 is Golden Tau 6.289211022059386.
Traditional Tau 6.283185307179586 says that if the circumference of a circle has 36000 equal units of measure then the radius of the circle is 5729.577951308232523 (reduced to 4 decimal places is 5729).
Alternatively traditional tau 6.283185307179586 says that if a circle has a circumference of 360 then the radius of the circle is 57.295779513082325 (reduced to 4 decimal places is 57.29)
Golden Tau 6.289211022059386 says that if the circumference of a circle has 36000 equal units of measure then the radius of the circle is 5724.088422813310602 (reduced to 4 decimal places is 5724).
Alternatively Golden Tau 6.289211022059386 says that if a circle has a circumference of 360 then the radius of the circle is 57.240884228133106 (reduced to 4 decimal places is 57.24)
It is a Geometrical fact that if one 8th of a circle’s circumference is multiplied by the square root of 1.618033988749895 (1.27201964951406) then the result is the measure for the radius of the circle. 1.27201964951406 is the ratio gained from dividing the second longest length of a Kepler scalene right triangle by the shortest edge length of the Kepler scalene triangle. If the radius of a circle is divided by one 8th of the circle’s circumference then the resulting ratio is the square root of 1.618033988749895 (1.27201964951406).
We can use the Pythagorean theorem to determine which value of Pi is correct out of Traditional Pi 3.141592653589793 or Golden Pi 3.144605511029693: en.wikipedia.org...
So if the circumference of the circle is 360 and one 8th of 360 is 45. So if the shortest edge length of a Kepler right triangle is 45 then according to the Golden ratio of Cosine (36) multiplied 2 = 1.618033988749895 the hypotenuse of the Kepler right triangle is 72.811529493745275. If the hypotenuse of a Kepler right triangle is divided by the shortest edge length of a Kepler right triangle then the result is the Golden ratio of Cosine (36) multiplied 2 = 1.618033988749895. 72.811529493745275 divided by the Golden ratio of Cosine (36) multiplied 2 = 1.618033988749895 is 45.
72.811529493745275 squared is 5301.518827218538062.
45 squared is 2025.
5301.518827218538062 subtract 2025 = 3276.518827218538062.
The square root of 3276.518827218538062 is 57.24088422813311. (reduced to 4 decimal places is 57.24).

So if the circumference of the circle is 36000 and one 8th of 36000 is 4500. So if the shortest edge length of a Kepler right triangle is 4500 then according to the Golden ratio of Cosine (36) multiplied 2 = 1.618033988749895 the hypotenuse of the Kepler right triangle is 7281.1529493745275. If the hypotenuse of a Kepler right triangle is divided by the shortest edge length of a Kepler right triangle then the result is the Golden ratio of Cosine (36) multiplied 2 = 1.618033988749895. 7281.1529493745275 divided by the Golden ratio of Cosine (36) multiplied 2 = 1.618033988749895 is 4500.
72.811529493745275 squared is 53015188.272185380623353.
4500 squared is 20250000.
53015188.272185380623353 subtract 20250000 = 32765188.272185380623353.
The square root of 32765188.272185380623353 is 5724.088422813311. (reduced to 4 decimal places is 5724).

a reply to: Deaf Alien

Another example is circumference of circle is 18. 18 divided by 4 = 4.5.
So we can get the measure for the diameter of a circle with a circumference of 18 by multiplying 1 quarter of 18 that is 4.5 by the square root of 1.618033988749895 (1.27201964951406) = 5.72408842281327.
Also we get the measure for the diameter of a circle by multiplying 1 quarter of the circle’s circumference by Tangent (51.82729237298776) degrees in Trigonometry. 4.5 multiplied by Tangent (51.82729237298776) degrees is 5.72408842281327 in Trigonometry.
Now I am going to prove that if the diameter of a circle is 5.72408842281327 and the diameter of the circle is divided into he Golden ratio of Cosine (36) multiplied by 2 = 1.618033988749895 and the division point extended to the circumference of the circle then a isosceles triangle that is made from 2 Kepler right triangles is created and the height of the isosceles triangle is 3.53768119990838. So the second longest edge length of each Kepler right triangle that are both half of the isosceles triangle have a measure also of 3.53768119990838. From the opposing pole of the diameter 2 smaller Kepler right triangles have hypotenuses that touch the circumference of the circle and the measure for both the hypotenuses of these 2 smaller Kepler right triangles is also 3.53768119990838.
Diameter of the circle = 5.72408842281327 subtract 3.53768119990838 = 2.18640722290489. 2.18640722290489 is the measure for the shortest edge lengths for the 2 smaller Kepler right triangles. There are a total of 4 Kepler right triangle inside of the circle.
2.781152949374527 is the measure for half the base width of the isosceles triangle that is made from the 2 larger Kepler right triangles.
2.781152949374527 is also the measure for the shortest lengths of each of the larger Kepler right triangles that make up the isosceles triangle that has a height of 3.53768119990838 and a base width of 5.562305898749054. 2.781152949374527 is half of 5.562305898749054.
Remember the Pythagorean theorem: en.wikipedia.org...
3.53768119990838 squared is 12.515188272185195.
2.781152949374527 squared is 7.73481172781463.
12.515188272185195 plus 7.73481172781463 = 20.25.
The square root of 20.25 is 4.5.
51.82729237298776 degrees is the usual measure angle for the hypotenuse of a Kepler right triangle while the other measuring angle for a Kepler right triangle is 38.17270762701226 degrees. 51.82729237298776 degrees is gained when the ratio 1.272019649514069 is applied to the inverse of the Tangent function in Trigonometry. 38.17270762701226 degrees is gained when the ratio 0.786151377757423 is applied to the inverse of the Tangent function in Trigonometry
Also 2.781152949374527 divided by Cosine (51.82729237298776) is 4.5.
4.5 is 1 quarter of 18. Remember again that 2.781152949374527 is half of the base width of the isosceles triangle and also the measure for the shortest edge lengths of the 2 Kepler right triangles that make the isosceles triangle.
Remember to divide the diameter of the circle into the Golden ratio of Cosine (36) multiplied by 2 = 1.618033988749895.
Circumference of circle is 18. Diameter of circle is 5.72408842281327.
Also if you create a Kepler right triangle that has its shortest edge length as 4.5 then the hypotenuse will be 7.281152949374528 and if the length of the hypotenuse 7.281152949374528 is divided into the Golden ratio of Cosine (36) multiplied by 2 = 1.618033988749895 then the larger part of the division of the Kepler right triangle’s hypotenuse into the Golden ratio of Cosine (36) multiplied by 2 = 1.618033988749895 is also 4.5.
7.281152949374528 divided by 1.618033988749895 is 4.5. Also 4.5 divided by Cosine (51.82729237298776) is 7.281152949374528. So if the shortest edge length of the Kepler triangle is 4.5 then the measure for the second longest edge length is 5.72408842281327. 5.72408842281327 is the measure for the diameter of a circle with a circumference of 18 remember, so if the shortest length of the Kepler right triangle is equal to 1 quarter of a circle’s circumference then the second longest edge length of the Kepler right triangle is equal to the measure of the circle’s diameter.
18 divided by 5.72408842281327 is Golden Pi = 3.144605511029693.
All you need is a compass and straight edge ruler and obviously a pencil and a pocket calculator.
Create a circle on a piece of paper and divide the diameter into the Golden ratio and then connect the division point with a straight line towards the circumference on either side of the division of the circle’s diameter into the Golden ratio.
I hope that you already know how divide a given line into the Golden ratio with just compass and ruler and obviously a pencil.

a reply to: CHiram_Abiff

Calculator confirmation for Golden Pi 3.144605511029693 values:
Please remember that if 1 eighth of a circle’s circumference is multiplied by the square root of 1.618033988749895 (1.27201964951406) the result is the measure for the radius of the circle and if 1 quarter of the circle’s circumference is multiplied by the square root of 1.618033988749895 (1.27201964951406) the result is the measure for the diameter of the circle.
If the measure of the circumference of a circle is already known but the length of the circle’s diameter is not yet known another solution is to multiply 1 quarter of the circle’s circumference by the square root of 1.618033988749895 (1.27201964951406) and the result will be the correct length of the circle’s diameter. The length of a circle’s diameter can also be gained from by multiplying 1 quarter of the circle’s circumference by Tangent 51.82729237298776 degrees in Trigonometry. If the circumference of a circle is divided by the diameter of a circle the resulting ratio is Pi. The accuracy of the value of Pi that you get is determined by how accurate the value for the square root of the Golden ratio that you have. The accuracy for the value of the square root of the Golden ratio is determined by the accuracy of the Golden ratio that you have.

If the measure of the diameter of a circle is already known but the measure of the circle’s circumference is not yet known another solution is to divide the circle’s diameter by the square root of 1.618033988749895 (1.27201964951406) and the result will be 1 quarter of the circle’s circumference so multiply 1 quarter of the circle’s circumference by 4 and the result is the measure for the circumference of the circle.

If 1 quarter of the circle’s circumference is multiplied by the square root of 0.618033988749895 (0.786151377757423) then the result is the larger measure of the circle’s diameter being divided into the Golden ratio of Cosine (36) multiplied by 2 = 1.618033988749895. Cosine (72) multiplied by 2 = 0.618033988749895 and the square root of 0.618033988749895 is 0.786151377757423.
Here is a description that you can test with a calculator for yourself: The circumference of the circle is 360 and 360 divided by 4 is 90. 90 divided by the Golden ratio of Cosine (36) multiplied by 2 = 1.618033988749895 = 55.623058987490531.
55.623058987490531 multiplied by the square root of 1.618033988749895 (1.27201964951406) = 70.75362399816759.
70.75362399816759 multiplied by the Golden ratio of Cosine (36) multiplied by 2 = 1.618033988749895 = 114.4817684562654.

114.4817684562654 is the measure for the diameter of the circle and 360 is the measure for the circle’s circumference.
360 divided by 114.4817684562654 is Golden Pi = 3.144605511029693.
Another example is circumference of circle is 12. 12 divided by 4 = 3.
So we can get the measure for the diameter of a circle with a circumference of 12 by multiplying 1 quarter of 12 that is 3 by the square root of 1.618033988749895 (1.27201964951406) = 3.81605894854218.
Also we get the measure for the diameter of a circle by multiplying 1 quarter of the circle’s circumference by Tangent (51.82729237298776) degrees in Trigonometry. 3 multiplied by Tangent (51.82729237298776) degrees is 3.81605894854218 in Trigonometry.
Now I am going to prove that if the diameter of a circle is 3.81605894854218 and the diameter of the circle is divided into he Golden ratio of Cosine (36) multiplied by 2 = 1.618033988749895 and the division point extended to the circumference of the circle then a isosceles triangle that is made from 2 Kepler right triangles is created and the height of the isosceles triangle is 2.358454133272253. So the second longest edge length of each Kepler right triangle that are both half of the isosceles triangle have a measure also of 2.358454133272253. From the opposing pole of the diameter 2 smaller Kepler right triangles have hypotenuses that touch the circumference of the circle and the measure for both the hypotenuses of these 2 smaller Kepler right triangles is also 2.358454133272253.
Diameter of the circle = 3.81605894854218 subtract 2.358454133272253 = 1.457604815269927. 1.457604815269927 is the measure for the shortest edge lengths for the 2 smaller Kepler right triangles. There are a total of 4 Kepler right triangle inside of the circle.

1.854101966249684 is the measure for half the base width of the isosceles triangle that is made from the 2 larger Kepler right triangles. 1.854101966249684 is also the measure for the shortest lengths of each of the larger Kepler right triangles that make up the isosclese triangle that has a height of 2.358454133272253 and a base width of 3.708203932499369. 2.358454133272253 is half of 3.708203932499369.
Remember the Pythagorean theorem: en.wikipedia.org...
2.358454133272253 squared is 5.562305898748974.
1.854101966249684 squared is 3.437694101250944.
5.562305898748974 plus 3.437694101250944 = 9.
The square root of 9 is 3.
51.82729237298776 degrees is the usual measure angle for the hypotenuse of a Kepler right triangle while the other measuring angle for a Kepler right triangle is 38.17270762701226 degrees. 51.82729237298776 degrees is gained when the ratio 1.272019649514069 is applied to the inverse of the Tangent function in Trigonometry. 38.17270762701226 degrees is gained when the ratio 0.786151377757423 is applied to the inverse of the Tangent function in Trigonometry
Also 1.854101966249684 divided by Cosine (51.82729237298776) is 3.
3 is 1 quarter of 12. Remember again that 1.854101966249684 is half of the base width of the isosceles triangle and also the measure for the shortest edge lengths of the 2 Kepler right triangles that make the isosceles triangle.
Remember to divide the diameter of the circle into the Golden ratio of Cosine (36) multiplied by 2 = 1.618033988749895.
Circumference of circle is 12. Diameter of circle is 3.81605894854218.
Also if you create a Kepler right triangle that has its shortest edge length as 3 then the hypotenuse will be 4.854101966249685 and if the length of the hypotenuse 4.854101966249685 is divided into the Golden ratio of Cosine (36) multiplied by 2 = 1.618033988749895 then the larger part of the division of the Kepler right triangle’s hypotenuse into the Golden ratio of Cosine (36) multiplied by 2 = 1.618033988749895 is also 3.
4.854101966249685 divided by 1.618033988749895 is 3. Also 3 divided by Cosine (51.82729237298776) is 4.854101966249685. So if the shortest edge length of the Kepler triangle is 3 then the measure for the second longest edge length is 3.81605894854218. 3.81605894854218 is the measure for the diameter of a circle with a circumference of 12 remember, so if the shortest length of the Kepler right triangle is equal to 1 quarter of a circle’s circumference then the second longest edge length of the Kepler right triangle is equal to the measure of the circle’s diameter.
12 divided by 3.81605894854218 is Golden Pi = 3.144605511029693.
All you need is a compass and straight edge ruler and obviously a pencil and a pocket calculator.
Create a circle on a piece of paper and divide the diameter into the Golden ratio and then connect the division point with a straight line towards the circumference on either side of the division of the circle’s diameter into the Golden ratio.

The problem with your original argument in the OP is that 1 is a rational and commensurable (countable) number, while .999~ (.9 repeating) is an irrational and incommensurable number.

So you are comparing apples and oranges.

It is true that you can't find a number larger than .999~ but smaller than 1, but that would be the same as asking to find an apple that is an orange.

I do say, old chaps...pip pip , ...cherrio....top drawer casting out nines

Please allow a tangent in this case......in a great thread about nines......how is we didn't come across casting out nines........

I gotta know....love

originally posted by: Box of Rain
The problem with your original argument in the OP is that 1 is a rational and commensurable (countable) number, while .999~ (.9 repeating) is an irrational and incommensurable number.

.999... is a rational number though! Every decimal number that has an eventually repeating decimal part is rational.
And we don't really use the words commensurable anymore. It was popular due to Euclid's treatment of numbers, but he didn't really understand the number system as well as we do now.