No.

You cannot integrate or differentiate any numbers. You an only integrate and differentiate functions, which are a very different thing from numbers.

Pi is hard to integrate currently because it moves off the page in 2D both in and out while you rotate with it. We don't see this when we draw a circle. We pretend that the exponential pi doesn't do this whereas a true representation of Pi would be a spiral in and then out of the page over 4 consecutive half turns.

This is the reason why Pi X R squared isn't Pi squared R squared which is what you would get with the constant of 7 or 10 or 200

Square, side 20cm, perimeter 80 cm, 400 cm^2

Square, side 200cm, perimeter 800 cm, 40000 cm^2

The square's magnitude gets squared and the UNITS change from cm to cm^2, same for volume to cm^3

Circle, side 20, perimeter 2Pi X 40, area Pi X 400cm^2

Circle, side 200, perimeter 2Pi X 400, area Pi X 40000cm^2

No unit change... Pi is an exponent of itself, not a constant in the normal way.

When you integrate dimensions or units they change from x to x^2, but not Pi. The only other unit that does this is our unit ---- 1 unit, if we used units of two, then the unit squared would have a square relationship. If we fixed Pi as the unit, 1 would become irrational with respect it.

That is why you use a unit. 2Pi is used as a unit everywhere as a constant. It seems to behave like one.

Yet it is Pi and not 4Pi^2 with the area of a circle compared to the circumference like with the other constants 20 and 200 they increase 10 fold and so did the unit, they got squared.

Pi is it own exponent in that if you multiply it by 2 it doubles. But when we double it (by making a circle with a radius twice that before), we differentiate Pi at the same time from 2Pi to 2pi/2 = pi.

That is why 2Pi does not behave like a normal constant.

And that is why Pi circles the square

The real numbers are a function of the unit number 1.

Have a look back at how they are constructed. The number line is constructed by an addition operator.

Doesn't include zero because zero subtracted from the next term or added to the previous terms doesn't get to either.

Some of you are calling me out, but are utterly wrong yourselves with your idea of units of measure and the true nature of calculus.

No, pi is hard to integrate because it is a number and not a function.

It sounds like you're referencing the construction of the natural numbers from the Peano axioms, but you've got it a bit muddled up.

In that system, the natural numbers are constructed from an empty set {}, which we define to be zero, and a successor function, s(x) = {x}.

So s(0) = s({}) = {{}}, or a set containing the empty set. This set is called 1.

And s(1) = s(s(0)) = {{{}}}, which we call 2.


Note here that 2 is not a function. 2 is a number which happens to be the product of a function. The function is the thing that takes a number as input and gives another number as an output.

Another caveat here is this successor function cannot be derived or integrated, either. It's a function that only operates on the natural numbers, and calculus only applies to functions that operate on the real numbers.

I'll wait to see if Kim was in the password and then I'll explain about the Fib sequence stuff because I missed out a bit of the transformation in the first post earlier today regarding the Fib numbers.

If KIM was in that password (and there were two in their one with a lower case n or m for the second term). But also a Q and a 3 so I'm not sure.

If the moderator who stopped the last discussion is here, my apologies if it seemed like a joke yesterday but it wasn't. I'm not unbalanced, pschizophrenic or godsquad.

Nobody has spotted the pattern in the primes, so I know what kind of claim I'm making, but it is not enough to explain the way I have and I'm sorry for the frustration that has caused.

I'm currently cracking a 60 year old code and it looks like its working. It seems that no matter how you encrypt, the "entropy" of the message remains like a "direction within the imaginary plane of the encrypted message orthogonal to the real plane." I know that last sentence is very abstract but it is fitting.

Ok, a function can be described as anything you like.

Function(x+1) = Function(x) + 1

How is that not the number line?

I think you have it wrong.

You construct those numbers like this

{}
{{}}
{{},{{}}}

Otherwise your two {{{}}} breaks down to the set of one element containing nothing which is the same as the first. The second one is the set of two elements that contain nothing.

The number line is a set of numbers.

A function is an entity that associates an input value with an output value.


Also, that bit algebraic transformation you gave as an example only works for a very special set of functions such as f(x) = x - 2.

I think you have it wrong, but I'm willing to run with this:

Try defining a version of the successor function that produces results in the manner you just described, and let's see how far we can go with it.


(The traditional successor function that all the abstract algebra textbooks contain wouldn't produce the progression you just described. Since s(x) = {x}, s({{}}) = {{{}}}. It's just putting another pair of brackets around whatever is passed in as x.)

I cannot believe you did that

"The number line is a set of numbers."

Each number has a distinct property that is repeated in that set for convenience. Each number is different (one property) and each number is different by one (another property) more than the other.

Nothing fancy about that?

One is quite fancy a number. How many other numbers have the same square and the square root?

Wow!! is that a pie?

Any chance you are really going to answer a lot of questions that I posed to you in your previous 3 threads on exactly the same silly subject as this one?

Don't bother to answer because I already know you are not going to do that.

And your lack in mathematical skills is blatantly apparent, and without any shame you just come back and back and back, with the same ridiculous stuff.

Talking about trolling!

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善數, 不用籌策 (shàn shù, bù yòng chóu cè)
He who is good at counting, uses no counting tools
“A good scientist has freed himself of concepts and keeps his mind open to what is”
道德經, 二十七 (dào dé jīng, 27)

It was more that YOU did not get that bit, Mr. Curtis, and no it does not make sense.

Oh ignorance is blissssss
Like Snoopy said "I am outrageously happy in my stupidity"

4^13 is about Pi^16?
4^13 = 67108864
Pi^16 = 90032220

So yeah, close but no cigar.

You are really making this up at the go, and we need not take this seriously.

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善數, 不用籌策 (shàn shù, bù yòng chóu cè)
He who is good at counting, uses no counting tools
“A good scientist has freed himself of concepts and keeps his mind open to what is”
道德經, 二十七 (dào dé jīng, 27)

Here's a Natural Number wiki page

As you can see, chriscurtis has it right. The successor function being S(a) = a U {a}Let's not jump to any conclusions

Not many people post a von Neumann ordinal definition correction, even regurgitated!

This thread is not easy to understand but is interesting... if there was a more clear approach with some explanations, it would be better.

As far as I'm concerned, Chris, keep it coming ! I want to see where this leads...

chriscurtis, your ascii tables are extremely difficult to follow since columns do not line up.
Please put code tags around them so you can be read, you have the idea so it's your duty to communicate it clearly.

As pzkpfw wrote


Second point, and this is serious. Do not start another thread on non-standard mathematics, stick with this one and answer pertinent questions asked of you in a timely manner or you will get suspended or banned.

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But at least my construction is the second one in the list.

Uhhhhh just because you don't write it down, the perimeter HAS a unit and it is cm (or rather m if you want to stay in SI).

so you should have written
Circle, radius 20 cm, circumference 2Pi X 20 cm, area Pi X 400 cm²

Circle, radius 200 cm, circumference 2Pi X 200 cm, area Pi X 40000 cm²

Not only do we see that there is a unit change from circumference (cm) to area (cm²) but we also notice that you had yet another math error with your "40" and "400" in the "perimeter".

Indeed Pi remains Pi, and good it is, but it is not a unit, the unit was cm, just like the square. It is only, that because a circle has no sides, but only a radius, that we have the conversion factor Pi.

For the rest, you still have to explain your "differentiation" from the other thread
x^2 -> x -> 1/x -> 1/x^2
you do see that the middle bold arrow is incorrect, or not?

Well, I will not be bothering you for the next few weeks, I am off on vacation.

TaDa!

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善數, 不用籌策 (shàn shù, bù yòng chóu cè)
He who is good at counting, uses no counting tools
“A good scientist has freed himself of concepts and keeps his mind open to what is”
道德經, 二十七 (dào dé jīng, 27)

Lui?!?!

A decent calculator will support parentheses, and will do operations in whatever order you specify using the parentheses.


Okay, lets tackle just this. You repeatedly say "the numbers get recycled every 4^64" or similar things. Show why this is so. If it is an assumption, show why you used that assumption. Also, math involves larger numbers all the time, even in real-world problems. For example, the number of protons and neutrons in the Earth is about 95 quadrillion times 4^64. Does this mean the Earth's mass of 5.97e24 kg is identical to a mass of just 5.65e11 kg? That's just 500 million metric tons. World production of steel exceeds 800 million tons. Are we really churning out over an Earth mass of steel each year with what we scrape out of the Earth's crust?

Pi is a constant, not a unit, not a function, not a variable. It behaves like any other constant under integration and differentiation, and any other mathematical operation.

The circle can be viewed as an infinitely-sided polygon, its area being equal to the sum of the areas of each triangular "slice". Each slice is an isosceles triangle, the length of its base proportional to pi (the ratio between the circumference of a circle and its diameter) and the diameter of the circle, and its height equal to the radius of the circle. The area of each triangle is thus:
A = 0.5*(r*2*pi/n)*r = r*r*pi/n = (pi*r^2)/n

And the sum area of n triangles is pi*r^2
See? No mystery to it. Nothing to do with numbers "cycling", or pi behaving differently under integration.

Thanks hhEb09'1 And it wasn't regurgitated, I just rush through things without correcting mistakes while my mind goes onto something else. I know set theory around the empty set like the back of my hand now. The only reason I stopped using it is most people don't understand what I'm talking about

This is part one of the Prime function formula

It shows the pattern of primes.

What you are looking for is the pattern BETWEEN the primes which is hidden yet much easier to spot.

The primes follow the growth pattern in the GAPS between the primes.

Fi 1,1,3

1st cycle 1,1,3

2nd cycle 13,13,135

3rd cycle 135,135,137

Prime numbers that grow out of the integers on the left and we want the GAPS between the primes that
make their pattern.

If the number does fit the gap it isn't prime.

three steps the same

one on, same again, scale up 2, then same as start.

1->1->3

next cycle, take last two steps and use it for the next cycle
[1->3][1->3][1->3][3->5]

next is
{[1->3][1->3][1->3][3->5]}{[1->3][1->3][1->3][3->5]}{[1->3][1->3][1->3][3->5]}

in steps of 1.1.:3.1.:3.1.:3.::5.:3.::5...3

R....Fi 1:1:3
1.
2...
3....p
4....-
5....p
6....-
7....p
8....-
9....-
10...-
11...p
12...-
13...p
14...-
15...-
16...-
17...p
18...-
19...p
20..-
21..-
22..-
23..p
24..-
25..-
26..-
27..-
28..-
29..p
30..-
31..p

Yep, thanks.

Hope you have a fabulous time! Anywhere nice?

Thanks

Here's what I mean

As the numbers we know approach 4^64 it is like coming to the end of a set of bits

I'll start simple

with 1 and 0

0,1,10,11,110,111,100

The size is 2. Every second step, the number of bits increases.

After 1 cycle, we have enough info to establish every detail of all the rest. Just one bit is enough to know where in the cycle we are.

Max info 2, after the first two changes we know the entire set.


Next 0, 1, 2

0,1,2,10,11,20,21,22,100

The size of the cycle is 3.

One more and and the cycles appear to be growing at N number of units. No matter how many bits we add there is no way to get any numbers that are new.

If I do this, it'll be more complete.

00000000,00000001,0000002,

Doesn't matter how many bits you have, its the number of units that determine the difference in numbers.

We have ten units. 01234567890

You assume that the property of this numbers changes after ten.

I'm saying that they don't.

You can know all the primes and all the relationships from whichever number of different units you have.

Numbers are important, we know the difference between them. It is the 9 digits that determine everything else.

We don't need that many. We know the change is the same between each unit, so all we need is the unit change over time of of those units as that will describe the whole nine.

134 -> m = magnitude change in units of size of the units 1 : 3 : 4 SPACE of the very small
123 -> 0 = units of objects 1 : 1 : 1 or our number line -> TIME
113 -> i = units of smaller scale change of 1 : 3 with our line SPACE we live in
112 -> e = units of smallest scale change of 1 : 2 SPACE of the very big

1:2:6:9

Even if we add more bits we will know the properties from how they are constructed.

So, more numbers no difference.

If you use the large units for measurements of circles (Pi is made of this unit) then you have the number system 1,3,4,5,7,8,10,11,13,14,15 etc every second change jumps two

In these units a circle has the ratio 3 length to diameter and the maths is easy for that. All the numbers work out.

Any time you see a 6 or a 9 in Pi in real life you are at 3 in the cycle but the circle is the square and cube of the previous one respectively.

A six unit is a scaled 3

So, you can have all the size of numbers you like, it doesn't take more than the different digits you have to describe what they can do.

Nope, not even close. Not even one character close.

Instead of trying to show all your numbers in mixed units, stick with one. It looks like your trying to mix binary and decimal and base 10 and base whatever comes to mind.

And as others have mentioned Pi is a constant, not a unit.

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Nope, not even close. Not even one character close.

Instead of trying to show all your numbers in mixed units, stick with one. It looks like your trying to mix binary and decimal and base 10 and base whatever comes to mind.

And as others have mentioned Pi is a constant, not a unit.

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"The universe is driven by the complex interaction between three ingredients: matter, energy, and enlightened self-interest." - G'Kar

Oops, sorry for the double post. This server needs an enema real bad.

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"The universe is driven by the complex interaction between three ingredients: matter, energy, and enlightened self-interest." - G'Kar

Well... he did say KIM or KIMKIM. So a double reply ain't all that bad

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Meet the OOONG TOE.

How is it like that? Why is it like that at 2^128, and not 2^32, or 2^256?


We have ten digits. Symbols for small counts, used together in a positional number system to represent numeric quantities. Units are something entirely different.


No I don't. The only thing special about 10 is that if I want to count higher, I have to start using my toes. Numbers are numbers. It does not matter how many digits it takes to represent them, that's just a matter of notation. If you have s different types of symbols and a string of n symbols, you can represent up to s^n different numbers, but those numbers exist whether you have room to represent them or not, and things like primeness are true no matter what symbols or how many you use.

You, on the other hand, make repeated reference to 4^64 as being somehow special. It's a big number, a minimum of 40 characters long in decimal format including the decimal point, 129 bits long in binary...and very simple in that base: 1 followed by 128 0's. 4^64 + 1 is 1 followed by 127 0's and another 1, just as 16 + 1 is 10000 + 00001 = 10001, or 17 decimal.

chriscurtis, as you appear as if you might respond to questions:

1) What is special about base 10? It is clearly special to you.

2) If f(x)=x^2, what do you get if you differentiate it once with respect to x? What do you get if you differentiate it again? What do you get if you do this a third time?

3) Demonstrate your claim about 4^64.

Between 111 and 100 the number of bits are constant, yet that's the step you're claiming should increase one.

You're stuffing a lot of ideas in each post, with a lot of your steps left out so noone can follow what you're thinking, especially since you're describing things in non-standard terminology.

Lets take things slowly so you can make others understand what you're talking about.

The sequence you have in the end of what I quoted, could you please give the exact rules you use to construct it, and also expand it to at least 20 elements.
As it stands there's no discernible rule to construct it, which makes discussing it meaningless.

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‘To those who regard “crime fiction” as some sacred icon which must follow a rigid formula, I will always be the man who writes 18-syllable haiku.’Trying to make sense of computers, The Error Log.