Deeper than primes

[epix]

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

Just sayin'

What are you saying? If you're saying that the kids got confused by idiotic symbolism that is strongly counterintuitive, then you are right.

 

[readme.txt]

What are you saying? If you're saying that the kids got confused by idiotic symbolism that is strongly counterintuitive, then you are right.

Not only the kids, I'd say. Pseudomathematicians too.

 

[epix]

Not only the kids, I'd say. Pseudomathematicians too.

Pseudomathematicians invented the symbolism out of their laziness. 0.999... simply implies a number whose fractional part comprise 9's the number of which approaches infinity. When 1, 2, 3, 4, ... shows up, no one talks any limits, so why should things be different with 0.999...?

 

[epix]

Here is an example of the fact that we may not see every arrangement there is, coz we can't be "omnifocused."

Doron, [text]

So you began to write a short letter/post to Doron. The nature of the text depends on what you want to say and the name that you've already written doesn't affect the composition of the text. But it can. Doron makes often ascriptions that are not immediately clear and here is a model of such.

Doron, 14_5

Assuming that the numerical assignment isn't random, the possible logical explanation to the choice of the numbers is that it applies to the last letter in the name: N is the 14th letter in the alphabet and the 5th one in the name. So substitute "text" in the brackets with both numbers:

Doron, [14_5]

Now you respond in kind. Would Doron be able to decode the symbolism, which says to look for a sentence that is made of 14 words where 5 of them include letter N? If he does, would you be able to compose such a sentence given the numerical restriction?

Again, stop simply trying to posit aspects of your own failed reasoning onto others.

Wow! That was fast.

 

[doronshadmi]

Here is an example of the fact that we may not see every arrangement there is, coz we can't be "omnifocused."

Doron, [text]

So you began to write a short letter/post to Doron. The nature of the text depends on what you want to say and the name that you've already written doesn't affect the composition of the text. But it can. Doron makes often ascriptions that are not immediately clear and here is a model of such.

Doron, 14_5

Assuming that the numerical assignment isn't random, the possible logical explanation to the choice of the numbers is that it applies to the last letter in the name: N is the 14th letter in the alphabet and the 5th one in the name. So substitute "text" in the brackets with both numbers:

Doron, [14_5]

Now you respond in kind. Would Doron be able to decode the symbolism, which says to look for a sentence that is made of 14 words where 5 of them include letter N? If he does, would you be able to compose such a sentence given the numerical restriction?



Wow! That was fast.

Epix, Traditional Math takes the palace value system as one of many methods of numerals' representation.

By following this notion, a numeral is not the number itself, so according this notion anyone who claims that, for example, the numeral 0.999…[base 10] is smaller than the number 1, simply shows (according Traditional Math) that he\she can't distinguish between the representation (place value method, in this case) and the represented (the number itself).

By following Traditional Math 1 = 0.999…[base 10] = …= 0.111…[base 2] , where in this case "=" simply says that number 1 has many representations that are numerals, where no numeral is actually the number 1 itself.

As long as Traditional Math understands the place value system as a representation method out of many other representations' methods, there can't be any dialog between OM (which claims that the place value is a system of numbers) and Traditional Math.

 

[doronshadmi]

Take for example this part, taken from http://en.wikipedia.org/wiki/Number :

When a real number represents a measurement, there is always a margin of error. This is often indicated by rounding or truncating a decimal, so that digits that suggest a greater accuracy than the measurement itself are removed. The remaining digits are called significant digits. For example, measurements with a ruler can seldom be made without a margin of error of at least 0.01 meters. If the sides of a rectangle are measured as 1.23 meters and 4.56 meters, then multiplication gives an area for the rectangle of 5.6088 square meters. Since only the first two digits after the decimal place are significant, this is usually rounded to 5.61

For example, number PI itself (which is not a Q member) can't be accuratly defined by place value mathod, which is alwasy based of collections of equale sizes upon infinitely many given scale levels (which is a property of Q members).

Such fractals simply can't define the accurate value of PI, as clearly seen in http://www.internationalskeptics.com/forums/showpost.php?p=6465716&postcount=12075 example.

But since Traditional Math understands the place value method as a system of numerals, it does not have any problem to use an expression like number "PI = numral 3.14...[base 10]", where "=" in this case means: "represented by ...".

------------------------------

OM is developed beyond the notions of Traditional Math about the concept of Number, and shows that the concept of Number of Traditional Math is the particular case of a collection of distinct 0() spaces on 1() space, where any given distinct 0() space is local w.r.t 1() space, and 1() space is non-local w.r.t any given distinct 0() space.

This novel notion is expressed by 1(0()), which is based on the novel notion of different levels of existence between fullness (that has no successor) and emptiness (that has no predecessor), so 1(0()) is actually under the following framework:

∞(
1(0())
)

 

[readme.txt]

Pseudomathematicians invented the symbolism out of their laziness. 0.999... simply implies a number whose fractional part comprise 9's the number of which approaches infinity. When 1, 2, 3, 4, ... shows up, no one talks any limits, so why should things be different with 0.999...?

I don't get why it is "laziness", but well, that's not really important. And I know 0.9(bar) = 0.999... = 1. That's for sure. I'm just saying only pseudomathematicians or kids/students say it's not.

I'm not here for the whole "Deeper than primes" debate (because I didn't read it and I'm still wondering what this is all about), I'm here for the 0.9(bar) = 1 debate.

P.S. Why is this thread in the "Religion" subforum?

 

[zooterkin]

P.S. Why is this thread in the "Religion" subforum?

It's "Philosophy"; well, it certainly isn't mathematics.

 

[readme.txt]

It's "Philosophy"; well, it certainly isn't mathematics.

Really? But I read some maths here and there. How is it philosophy?

 

[doronshadmi]

Really? But I read some maths here and there. How is it philosophy?

Hi readme.txt,

This thread is here exactly because of what you say:

And I know 0.9(bar) = 0.999... = 1. That's for sure. I'm just saying only pseudomathematicians or kids/students say it's not.

For better understanding, please look at:

http://www.internationalskeptics.com/forums/showpost.php?p=6468807&postcount=12085

http://www.internationalskeptics.com/forums/showpost.php?p=6469003&postcount=12086

 

[doronshadmi]

Let's show the first 7 levels of the non-strict number 3.141592 …[base 10] < PI.

PI is shown by the green vertical line, and it is clear that 3.14…[base 10] < PI even if there are infinitely many places after the redix point (http://en.wikipedia.org/wiki/Radix_point).

The reason is very simple:

The place value system is based on equal sizes that exist upon infinitely many scale levels, and such a system simply can't be an accurate measurement tool of any irrational number.

But Traditional Mathematics does not care about this fact, because according to its notion, the place value method is no more than a numeration (some representation technique, out of many other representations) and not the number itself.


------------------------------

Again,

OM is developed beyond the notions of Traditional Math about the concept of Number, and shows that the concept of Number of Traditional Math is the particular case of a collection of distinct 0() spaces on 1() space, where any given distinct 0() space is local w.r.t 1() space, and 1() space is non-local w.r.t any given distinct 0() space.

This novel notion is expressed by 1(0()), which is based on the novel notion of different levels of existence between fullness (that has no successor) and emptiness (that has no predecessor), so 1(0()) is actually under the following framework:

∞(
1(0())
)

 

[epix]

I don't get why it is "laziness", but well, that's not really important. And I know 0.9(bar) = 0.999... = 1.

The reason why you "know" that 0.999... = 1 is simple:

Many are persuaded by an appeal to authority from textbooks and teachers...

The symbolic rendition 0.999... = 1 is a short of the full representation that starts bellow:

0.999... = (10ⁿ - 1)/10ⁿ where n → ∞.

When you substitute n in the formula with 1, 2, 3, 4, the result is 0.9, 0.99, 0.999, 0.9999 respectively. Obviously, substituting n with positive integer that approaches infinity results in a number that can be rendered as 0.999.... The ellipses indicate that the 9's will repeat ad infinitum. This number is always smaller than 1, but . . .

lim[n → ∞] (10ⁿ - 1)/10ⁿ = 1

The above identity says that the limit of the expression equals 1; it doesn't say that in some moment, as n approaches infinity, 0.999... suddenly becomes identical to integer 1. But in practical applications, such as in calculus, various limits are treated as an exact representation of the results that involve numbers that are approaching certain values through a convergence, but never reach them. The margin of error is simply "infinitely small", and can be safely neglected. No one ever went wrong by doing so.

There are surely kids out there who now believe that 0.999... as a number where the 9s repeat infinitely doesn't simply exist and that Doron has been right after all saying that a straight line has "blind spots" -- that there are segments on that line that cannot be covered by points.

 

[doronshadmi]

The reason why you "know" that 0.999... = 1 is simple:


The symbolic rendition 0.999... = 1 is a short of the full representation that starts bellow:

0.999... = (10ⁿ - 1)/10ⁿ where n → ∞.

When you substitute n in the formula with 1, 2, 3, 4, the result is 0.9, 0.99, 0.999, 0.9999 respectively. Obviously, substituting n with positive integer that approaches infinity results in a number that can be rendered as 0.999.... The ellipses indicate that the 9's will repeat ad infinitum. This number is always smaller than 1, but . . .

lim[n → ∞] (10ⁿ - 1)/10ⁿ = 1

The above identity says that the limit of the expression equals 1; it doesn't say that in some moment, as n approaches infinity, 0.999... suddenly becomes identical to integer 1. But in practical applications, such as in calculus, various limits are treated as an exact representation of the results that involve numbers that are approaching certain values through a convergence, but never reach them. The margin of error is simply "infinitely small", and can be safely neglected. No one ever went wrong by doing so.

There are surely kids out there who now believe that 0.999... as a number where the 9s repeat infinitely doesn't simply exist and that Doron has been right after all saying that a straight line has "blind spots" -- that there are segments on that line that cannot be covered by points.

OM does not agree with the notion that a given existing space is completely covered by any given previous existing space, and it does not matter if the considered spaces are strict or non-strict.

Such a notion is strictly developed beyond the notion of Limit, and it is based on the difference between Locality and Non-locality, which can't be comprehended by the reasoning that defines Limits.

The reasoning of Limits can't comprehend the place value system as numbers, because it has no understanding of different levels of existence between Emptiness (that has no predecessor) and Fullness (that has no successor).

Even if we ignore the place value system, the notion of distinct 0() spaces along 1() unconditionally leads to the conclusion that there are distinct 0() spaces along 1() only if there is ≠ between them, and ≠ is clearly free of any 0() space, otherwise no two arbitrary distinct 0() spaces along 1() can be defined.

 

[jsfisher]

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



Just sayin'

You, sir or madam, are trivializing Doron's breath and depth of cognitive limitations.

 

[epix]

The reasoning of Limits can't comprehend the place value system as numbers, because it has no understanding of different levels of existence between Emptiness (that has no predecessor) and Fullness (that has no successor).

Doron, it's "limits" not "Limits," therefore a limit cannot join the OM gods that you named Fullness and Emptiness and engage in some lewd act of reasoning. Change the letter case and you find out that limits don't have a mind to comprehend anything -- the folks who use them do.

The limits are essential in calculus. Without them, there would be no calculus and without calculus we would be on the same scientific level when there was no calculus.

You used inequality 3.1415... < Pi. How do you know what the decimal digits of Pi look like? Did you go through the result of the "traditional math" and simply copied them? Why don't you let Fulness and Emptiness get closer to the exact value of Pi, which will always remain unknown?

You think that there is no difference between rational and irrational numbers as far as the approximate value is concerned, and that the approximate value of Pi is getting more precise through 3, 3.1, 3.14, 3.141 and so on, but it doesn't go like that. The ever-more precise approximate form is a result of various summation formulas, and Pi is the limit when the number of summands is approaching infinity. One of the summation formula is the simple looking one that Euler came up with, and it goes like this:

pi = √[6*(1/1² + 1/2² + 1/3² + 1/4² + ...)]

It is said to approach Pi very slow, so I became curious how slow and found out that a dead snail is faster. It takes about ten million additions to get the first seven digits right!

The very first value is √6, which is 2.449....

So I wonder if Fullness and Emptiness can churn out a formula that outruns the one Euler came up with. Organic Mathematics shouldn't rely on the obsolete traditional approach; it should come up with its own version to account for the approximate rendition of number Pi, right?

 

[doronshadmi]

Organic Mathematics shouldn't rely on the obsolete traditional approach; it should come up with its own version to account for the approximate rendition of number Pi, right?

You are still missing the fact that according OM, no given space ( whether it is strict ( like 0.999[base 10]() or PI() ),
or non-strict ( like 0.999…[base 10]() or 3.14...[base 10]() ) ) is defined by other spaces.

All you have to do is to get the difference between (just for example) non-complex spaces like:

∞(
0(),0.999…[base 10](),1(),2(),3(), PI()…
)

and complex results like:

∞(
... PI(3(2(1(0.999…[base 10](0()))))) ...
)

Traditional Math can't comprehend that "≠" is the non-local property of 1() w.r.t 0().

Furthermore, Traditional Math actually claims that 1() is completely covered by 0() , which is equivalent to the claim that (for example) variable x ( where x is any arbitrary distinct 0() of [0,1] ) is both ≤ 1 OR both ≥ 0.


--------------

Again,

OM does not agree with the notion that a given existing space is completely covered by any given previous existing space, and it does not matter if the considered spaces are strict ( for example: PI() ) or non-strict ( for example: 3.14...[base 10]() ).

Such a notion is strictly developed beyond the notion of Limit, and it is based on the difference between Locality and Non-locality, which can't be comprehended by the reasoning that defines Limits.

The reasoning of limits can't comprehend the place value system as numbers, because it has no understanding of different levels of existence between Emptiness (that has no predecessor) and Fullness (that has no successor).

Even if we ignore the place value system, the notion of distinct 0() spaces along 1() unconditionally leads to the conclusion that there are distinct 0() spaces along 1() only if there is ≠ between them, and ≠ is clearly free of any 0() space, otherwise no two arbitrary distinct 0() spaces along 1() can be defined.

The limits are essential in calculus. Without them, there would be no calculus and without calculus we would be on the same scientific level when there was no calculus.

What is called traditional calculus, is simply a system that uses techniques which avoid non-strict results.

It does not mean that there can't be an extension of that system, which also deals with non-strict results, such that (for example)
1 - 0.999…[base 10] = 0.000…1[base 10]

 

[doronshadmi]

By the way, OM is different than the notion of Infinitesimals ( http://en.wikipedia.org/wiki/Infinitesimal ) or the notion of Non-standard analysis ( http://en.wikipedia.org/wiki/Non-standard_analysis ) which uses Infinitesimals, because the Infinitesimals are still taken as strict numbers , such that there is a strict number h that is smaller than all positive 1/n, and 1/h > any positive R member.

 

[The Man]

Some reading problems?

Just yours, as usual.

The considered number is smaller than any arbitrary number of (0,1] AND it is also > 0.

In other words, this considered number is not 1 AND it is not 0.

Again the interval (0,1] doesn’t restrict a member of the resulting set from being 1 while the interval (0,1) does.

 

[doronshadmi]

Again the interval (0,1] doesn’t restrict a member of the resulting set from being 1 while the interval (0,1) does.

Unless it is clearly written that the considered member is smaller than any arbitrary number of (0,1], where 1 is one of these arbitrary numbers, and you simply can't get it.

 

[epix]

By the way, OM is different than the notion of Infinitesimals ( http://en.wikipedia.org/wiki/Infinitesimal ) or the notion of Non-standard analysis ( http://en.wikipedia.org/wiki/Non-standard_analysis ) which uses Infinitesimals, because the Infinitesimals are still taken as strict numbers , such that there is a strict number h that is smaller than all positive 1/n, and 1/h > any positive R member.

The greatest and defining difference between Organic Mathematics and contemporary mathematics is that the former is purely intuitive and the latter is purely analytic.