Huge numbers

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Huge numbers

Postby PWrong » Wed Apr 28, 2004 12:02 pm

Exponential number line, hey? How would that work? Is there actually an accepted theory about this sort of thing? I can't imagine how such a broad subject could be ignored by mathematicians.

Split from "Its all wrong...ALL OF IT..." by Rob.
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Postby Keiji » Wed Apr 28, 2004 4:39 pm

ATM the only use I could see of an exponential number line is for scaling objects up into the 4th, 5th, 6th... nth dimensions.
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Postby PWrong » Thu Apr 29, 2004 1:05 pm

wow. It took 5 pages, but we've finally got to the topic of extra dimensions!

I was just wondering, why are there exactly three different operators like this? +, * and ^ have a few things in common, so could there be a fourth kind, like a "#"? This wouldn't be the same as the fourth dimension, because the fourth power takes care of that. So maybe there's something more fundamental than the number of dimensions.

Say, for example, a#b = a^a^a^... b times.
So 3#4= 3^3^3^3
Obviously, the numbers get huge very quickly.

You can use logs on these, e.g.

x#4 = e^(ln(x#4)) = e^(x^3*ln(x))

Is any of this feasible?
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Postby Keiji » Thu Apr 29, 2004 4:28 pm

That to me has no use.

However, I have had a idea for a new operator for ages. The perfect power operator. What this does is it finds the nth power of a number that is a perfect power, ie the exponent is also either a perfect power of the number, the number itself or 1.

EG:

2^2 = 4, so 4 is a perfect power of 2.
2^4 = 16, so 16 is also a perfect power of 2 (because 4 is perfect).
2^16 = 65536, so 65536 is also a perfect power of 2.

2^3 = 8 is NOT a perfect power of 2 because 3 is not 1 or 2 and is not a perfect power of 2.

The way this would work is:

2#1 = 2^1
2#2 = 2^2
(2#2.5 would be 2^3, if you were wondering.)
2#3 = 2^4 = 2^(2^2)
2#4 = 2^16 = 2^(2^(2^2))
2#5 = 2^65536 = 2^(2^(2^(2^2)))
etc.

For 3, it would go:

3#1 = 3^1
3#2 = 3^3
3#3 = 3^27 = 3^(3^3)
etc.
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Postby PWrong » Sat May 01, 2004 4:02 pm

That sounds really interesting, but I can't see any use for that either. I mentioned mine because it seems to be the next basic operator.

a*b = a+a+a... b times
a^b = a*a*a... b times
Surely the next operator should follow this pattern? I found a function called the "power tower" on a math website, but it didn't reveal much about it.

I also found it interesting because raising to the nth power implies n dimensions, so the next operator must imply something different. Since n dimensions means n coordinates needed to describe a location, what if you need two or more values to describe the number of dimensions? For instance, the same object could be 2D and 3D at the same time. I know it's pointless to pursue something so difficult to visualise, but it might be worth a try.
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Postby Keiji » Sat May 01, 2004 4:59 pm

Well, this is weird. 2#5 in my description is, according to Windows Calculator:

Code: Select all
2.0035299304068464649790723515603e+19728


Yet 2#4 is only 65536?
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Postby Keiji » Sat May 01, 2004 5:17 pm

Okay, a report on 10#N numbers:

10#1 = 10
10#2 = 10,000,000,000 = 1E+10
10#3 = 1E+10,000,000,000 = 1E+(1E+10)
10#4 = 1E+(1E+(1E+10))

Etc.

I think I may have found a way to store huger numbers than can be stored with scientific notation.

Let's see...

10!#100,000 = 1.5
so 10!#1,000 = 1.25
so 10!#100 = 1.183r

so 2,000 = (10#1.25)*2
so 509,000 = (10#1.25)*9 + (10#1.5)*5

Obviously this would be useless for "small" numbers like 509,000, but what about...

2.5E+10,000,000,000 = (10#3)*2.5

Much shorter!

I don't see much of a reason for anyone to use this, though. Maybe someone wants to know the number of atoms in a volume of 1 light-year[sup]3[/sup]? (lol)
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Postby PWrong » Tue May 04, 2004 11:02 am

It might be useful for measuring the size of the universe using the Planck Length as a unit instead of meters. Or maybe finding the volume of a higher dimensional universe.

Sorry to change the subject, but I have a question a bit like the "i^i" one earlier. I came across an annoying constant in Calculus about a week ago.

Start with any number, real or complex. Take the natural log of it, then take the natural log of the answer, and the take the natural log again and so on. No matter what number you started with, you should eventually get about
0.31813 + 1.3372i

Does anyone know how to get that as an exact value? All I can work out is that e^z = z
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Postby Keiji » Tue May 04, 2004 3:51 pm

PWrong wrote:It might be useful for measuring the size of the universe using the Planck Length as a unit instead of meters. Or maybe finding the volume of a higher dimensional universe.


Well, off you go and find out exactly how big each of these universes are and I'll happily convert them to hash format for you. XDDD
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Postby Geosphere » Thu May 06, 2004 6:03 pm

If anyone figures a way to measure the size of the universe, I don't care if its hectares, meters or furlongs, I think they get a Nobel Prize.
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Postby elpenmaster » Fri May 07, 2004 4:42 am

is there any formula for determining what n! is?
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Postby Keiji » Fri May 07, 2004 4:19 pm

n! = 1 * 2 * 3 * 4 * ... * n :wink:
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Postby elpenmaster » Sun May 09, 2004 4:33 am

yes, i know that n! = 1*2*3*4. . .*n
but i was wondering if there was a "shortcut formula" for it :)

for example, the shortcut formula for 1+2+3+4. . .+n is:

((absolute value of n)/(n))(1/2 (n squared))+((absolute value of n)/(n)(1/2 n)

instead of adding up all the numbers, you can just use the formula. is there anything like that for n! ?

by the way, what is the symbol used for 1+2+3+4. . .+n ?
:?
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Postby Keiji » Sun May 09, 2004 6:25 am

no, calculators do it with iteration
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Postby RQ » Mon May 10, 2004 3:41 pm

I dont think any of these things have anything but to shorten operations which aren't used by anything YET. for example it would be 2^2 times 2^2 that would be 2#2, but I dont think people would need that yet.
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Postby Rybo » Tue May 25, 2004 9:29 pm

elpenmaster wrote:thus, infinityx0=1
since 0 times infinity equals 1, then logically 1/0 equals infinity
this all is logical if you use a circular number line.
:D


Elpen, Infinity, or an infinite amount of numbers, is not a number i.e. it is beyond numeration ergo it is inumerable and is often icorrectly used in conjunction with words like small or large.

More aproproiatly is to say that we may have micro-infinity-- in as in "negating away from the postive numeration") or macro-infinity-- out as in "postively away from the negative numeration" --.

The number one(1) can be viewed as the one set of all concieved numbers from the historical records of humans, which, includesthe largest finite number ever concieved by a human or group of humans.

Zero is the opposite of that one(1)-set of numebers ever thought of and ocmmunicatted to self or others, in all known history to present.

In this scenario one(1) is a finite set of numbers and zero is an empty set of numbers. 1/0 = 0 not infinity.

Infinity is a concept that, like the empty, zero, nothingess metaphysical, 3-D space, outside of phyical Universe, is an infinity thereof or maybe it should be stated as infinitely empty space(zero) or as empty set( zero)

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Postby elpenmaster » Wed May 26, 2004 4:48 am

yes, i agree that infinity is "beyond large" and is, in short, *infinite*
however, you must realize that when dealing with a circular number line,
zero is just the opposite of infinity. . . infinilty small. when you multiply infinitly small by infinitly big, you cross out the infinites and get small times big, and you average out the small and big to get medium. on a circular number line, 1 is the medium number, so infinity times zero equals 1
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Postby PWrong » Thu May 27, 2004 2:19 pm

I'm not sure that zero is the same as infinitely small. In calculus, "Infinitely small" is the limit of x as x approaches zero. It's not the same as exactly zero, because you can still divide by it.

Try graphing y= x/x
It's just a horizontal line, but with a bit missing at x=0. But the limit as x approaches 0 is equal to 1. Everyone probably already knows this, but I'd like to restore some accepted mathematics to this discussion, to remind everyone that people have talked about all this for centuries, and it doesn't get them anywhere.

By the way, who first suggested the circular number line?
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Postby meanstotheend » Thu Jun 03, 2004 9:43 pm

lol, i made like the most popular strand in this forum :D
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Postby Geosphere » Fri Jun 04, 2004 3:00 am

Yes, but its original intent is long lost...
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Re: Its all wrong...ALL OF IT...

Postby Euclid » Fri Jun 04, 2004 3:01 am

meanstotheend wrote:It seems to me that everyone in the "modern" world of science is becoming fanatical, much as religious fanatics. I am proud to say that i am neither. EVERYONE SEEMS TO BE HUNG UP ON ABSOLUTES...I simply wanted to state that nothing is absolute.
Any and all comments are welcome!


You would probably be happier on a philosophy board.
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Postby elpenmaster » Fri Jun 04, 2004 6:24 am

i think that i first suggested the circular number line on this forum.
but i know that other people already had that idea before me

what is the reason that zero is not infinitly small? in calculus maybe there are limits and such to make it easier to figure things out, but. . . :D
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Postby Euclid » Sat Jun 05, 2004 1:10 am

elpenmaster wrote:i think that i first suggested the circular number line on this forum.
but i know that other people already had that idea before me


Yes, it's called a modulo system.

what is the reason that zero is not infinitly small? in calculus maybe there are limits and such to make it easier to figure things out, but. . . :D


In a way, zero is infinitely small. In the limit, as X approaches zero, does not 1/x go to infinity? Another way to look at this is to take something and cut it in half (Zeno's paradox). Now cut it in half again, and again...do you ever have nothing left? When you take whatever arbitrary piece you have and toss it away, then you have zero.[/quote]
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Postby Rybo » Sat Jun 05, 2004 3:22 am

Euclid wrote:In a way, zero is infinitely small. In the limit, as X approaches zero, does not 1/x go to infinity? Another way to look at this is to take something and cut it in half (Zeno's paradox). Now cut it in half again, and again...do you ever have nothing left? When you take whatever arbitrary piece you have and toss it away, then you have zero.


Euclid, this taking the finite physical Universe and multiplying it by divsion.

The number one-- or some number --, is a mathematically metaphysical concept;
1) of a finite set of one or more,
2) a notational place counter of some numeber
3) a binary place counter as on or off

Zero is a mathematically metaphysical concept of;
1) and empty set
2) no sets
3) a metaphysical concept ergo of itself
4) infinte nothing outside and beyond the one(1) finite physical Universe.

This latter statement above may be inclusive to "no sets". Im not much of a mathematician.
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Postby PWrong » Sun Jun 06, 2004 7:55 am

You can't say that 1/0= infinity
The answer is "infinite solutions", not just infinity.
I'm pretty sure that 1/infinity isn't exactly zero. They have words like "infinitesimal" for that. It's something like 0.00000 reccurring, with a hypothetical "1" on the end. It really doesn't matter which way you look at it, infinity isn't consistent with the universe.

Here's two more interesting properties of infinity/zero

1. There is more than one type of infinity.
There are as many even numbers as integers, but there are more real numbers than there are integers. The infinity of real numbers is larger than the infinity of integers.

2. You can make numbers out of nothing.

Take the empty set, {}
This represents 0
Now make a set that contains the empty set as a member, {{}}.
This is different from {}, so it represents 1
Now you can make any number, for instance, {{},{{}},{{{}}}} represents 3

Does anyone remember Douglas Adams's proof that the population of the universe is 0, assuming that space is infinite?

"Some simple facts about the universe"
Area: infinite.
Exports: None
Imports: None
Population: None
Since space is infinite, there are infinite places where life can exist. Therefore the population of each habitat is the total population divided by the number of habitats. Now any finite number divided by infinity is as close to zero as leaves no odds, so therefore the average population in any place is zero, therefore the total population of the universe is zero and any people you happen to meet are simply the products of a deranged imagination.
Art: None. The function of art is to hold the mirror up to nature, and there simply isn't a mirror big enough.
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Postby Euclid » Wed Jun 09, 2004 3:58 pm

PWrong wrote:"Some simple facts about the universe"
Area: infinite.
Exports: None
Imports: None
Population: None
Since space is infinite, there are infinite places where life can exist. Therefore the population of each habitat is the total population divided by the number of habitats. Now any finite number divided by infinity is as close to zero as leaves no odds, so therefore the average population in any place is zero, therefore the total population of the universe is zero and any people you happen to meet are simply the products of a deranged imagination.


For longer than I can remember, I have thought of mathematics in terms of a number line. I sort of quiescently sit at zero and then venture out from there depending on what I am doing. Horizontal motion takes me positively and negatively through the integers and reals--to me, infinity is just way off in the murky distance further than I can see. I just move vertically, up or down, and now I am moving in the plane. A simple paradigm shift puts me into complex numbers and adding another axis (z) let's me get to 3-space. Things fall apart after that. Sometimes I visualize space-time as the 3-space moving in time. After that, the visuals depart and I am left with algebra (either vector calculus or matrix theory). The point of all this is that you can do a lot just hanging around the corner, where everything comes to a point, the singularity, zero.

You can make it as metaphysical as you like, whatever turns you on, the reality is that you are here and you will only be here for a very short time. The only way you are going to get anywhere close to infinity is in your mind.
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Postby Polyhedron Dude » Wed Jun 09, 2004 10:23 pm

PWrong wrote:That sounds really interesting, but I can't see any use for that either. I mentioned mine because it seems to be the next basic operator.

a*b = a+a+a... b times
a^b = a*a*a... b times
Surely the next operator should follow this pattern? I found a function called the "power tower" on a math website, but it didn't reveal much about it.

I also found it interesting because raising to the nth power implies n dimensions, so the next operator must imply something different. Since n dimensions means n coordinates needed to describe a location, what if you need two or more values to describe the number of dimensions? For instance, the same object could be 2D and 3D at the same time. I know it's pointless to pursue something so difficult to visualise, but it might be worth a try.


The operator you refer to is known as tetration, also known as hyper4 operator and power towers. Of course you can also extend the concept and generate higher operators such as pentation, hexation, etc. To learn more do a google search on Graham's Number - it is so huge that to represent it, it would require 63 iterations of the following sequence:

1. 3 {5} 3 (represents 3 pentated to 3)
2. 3 {above number} 3
3. 3 {above number} 3, etc.

I have investigated huge numbers, and have generated a notation that I call Array Notation - it generates numbers that blow Graham's number away. For example in my notation {a,b,c} represents a {c} b or a "c-ated" to b. {3,3,5} would be 3 to the power of itself over 7 trillion times. My notation doesn't stop at operators but goes beyond into levels of operators, level of levels of operators, and level of level of levels, etc - and this is only the 1-D counterpart to the notation. {3,3,3,3} would be 3 powerexploded to 3 where powerexplosion is the third operator of the 3rd level - I call this number tetratri - it makes Graham's number look like nothin. My array notation not only deals with 1-D arrays, but can deal with multidimensional arrays or even tetration space arrays - the number's produced are unspeakably enormous. One of my favorites is gongulus - it is the number generated by a 10^100 array of 10's. A gongulusplex is the number generated by a 10^gongulus array of 10's.

Here are a few other number names I coined:
gaggol = {10,100,5}
tridecal = {10,10,10}
general = {10,10,10,10}
xappol - generated by 10x10 array of 10's
kungulus - generated by 10 {5} 100 array of 10's

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Postby Rybo » Thu Jun 10, 2004 1:08 am

Euclid wrote:
PWrong wrote:


For longer than I can remember, I have thought of mathematics in terms of a number line. I sort of quiescently sit at zero and then venture out from there depending on what I am doing. Horizontal motion takes me positively and negatively through the integers and reals--to me, infinity is just way off in the murky distance further than I can see. I just move vertically, up or down, and now I am moving in the plane. .


HI Euclid, if I may suggest you check out this site for differrent viewpoint on arriving at a metaphysical point using planes.
http://www.codefun.com/Geometry_quantum.htm

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Postby Rybo » Thu Jun 10, 2004 1:53 am

Polyhedron Dude wrote:
PWrong wrote:That sounds really interesting, but I can't see any use for that either. I mentioned mine because it seems to be the next basic operator.
.


I have investigated huge numbers, and have generated a notation that I call Array Notation - it generates numbers that blow Graham's number away. One of my favorites is gongulus - it is the number generated by a 10^100 array of 10's. A gongulusplex is the number generated by a 10^gongulus array of 10's.

Here are a few other number names I coined:
gaggol = {10,100,5}
tridecal = {10,10,10}
general = {10,10,10,10}
xappol - generated by 10x10 array of 10's
kungulus - generated by 10 {5} 100 array of 10's

Polyhedron Dude


Hey PD, You may want to check out Fullers cahnge numerating teechiques at
http://www.rwgrayprojects.com/synergeti ... p3100.html
and http://www.rwgrayprojects.com/synergetics/s12/p3830.html#1238.70
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Postby jinydu » Thu Jun 10, 2004 5:41 am

Here is a website that explains "tetration" and related topics:

http://home.earthlink.net/~mrob/pub/math/largenum.html

Just one question: How do I become a Tetraspace citizen?
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