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#1 This is Cool » What's so super about it? » 2009-03-31 11:56:05

MrRHQ
Replies: 1

This branch of mathematics I found recently is about tetration, super roots, and super logs. To bad we can't call it super power because that's already a term for something else lol. You just raise the exponent by the about of times by itself (minus 1 time). For the fifth hyper term, I think mathematicians need a new term instead of just using superscript numbers. I think with huge numbers is really not every lifestyle type of thing but more of a universal thing. Scientists use the scientific format to represent huge or small numbers so what is this mathematics useful for? By the way, we'll also need a name for this special system because there may be numbers that cannot equal tetriated terms. Like a real number multiplied by itself cannot be a negative number, there has to be more to understand of this.

What If I had this function:

f(x) = (5^5)?(5^2)/(5*2)-(5+2)

The ? is the unknown operator which is a level above division. Does it exist?
If we say that n^2/n = n and 2n-n = n then (n^n)?n = n.

Any input?

#2 Coder's Corner » Complex statistics functions in a C.P.R » 2009-03-19 18:06:00

MrRHQ
Replies: 0

(C.P.R stands for common programming language. C, C++, Java, Python, and more.)

OK, I want to know how functions like gamma and zeta which gamma uses integrals and zeta uses something related to the harmonic series but with the denominator as an exponential function.

I've looked up statistics functions in a common programming language made using only operators and variables. This means it can be Game Maker compatible which is what I'm looking for.

The gamma function on THIS WEBSITE is written in C++. The following below is a version I rewrote for Game Maker, credit goes to original creator though.

if!(is_real(argument))return 0;
var i,k,m,g,ga,gr,r,c,z;
g[0]=1.0;
g[1]=0.5772156649015329;
g[2]=-0.6558780715202538;
g[3]=-0.0420026350340952;
g[4]=0.1665386113822915;
g[5]=-0.0421977345555443;
g[6]=-0.009621971527877;
g[7]=0.007218943246663;
g[8]=-0.0011651675918591;
g[9]=-0.0002152416741149;
g[10]=0.0001280502823882;
g[11]=-0.0000201348547807;
g[12]=-0.0000012504934821;
g[13]=0.000001133027232;
g[14]=-0.0000002056338417;
g[15]=0.000000006116095;
g[16]=0.0000000050020075;
g[17]=-0.0000000011812746;
g[18]=0.0000000001043427;
g[19]=0.0000000000077823;
g[20]=-0.0000000000036968;
g[21]=0.00000000000051;
g[22]=-0.0000000000000206;
g[23]=-0.0000000000000054;
g[24]=0.0000000000000014;
z=argument;
if(z==z div 1){
    c=1;
    z-=1;
    repeat(z-1){
        c*=z;
        z-=1;
        if(z>=9223372036854775808){
            show_error("Error in function gamma().",0);
            exit;
        }
    }
    return c-(z<=0);
}else{
    if(abs(z)>1){
        c=abs(z);
        m=floor(c);
        r=1;
        for(k=1;k<=m;k+=1){
            r*=(z-k);
        }
        c-=m;
    }else c=z;
    gr=g[24];
    for(k=23;k>=0;k-=1){
        gr*=c;
        gr+=g[k];
    }
    ga=1/(gr*c);
    if(abs(z)>1){
        ga*=r;
        if(z<0)
            ga=-pi/(z*ga*sin(pi*z));
    }
}
if(ga>=9223372036854775808){
    show_error("Error in function gamma().",0);
    exit;
}
return ga;

It works, but I want to know how.
Brief analysis says that it looks like an array of random real numbers are initialized in the beginning. We can say that gamma(z) = z! when z is a natural number. Otherwise, we do some calculations. Since this is an integral related function, we multiply when using for loops I guess.

But, have you looked at the C++ gamma(); function? Is another algorithm faster than using arithmetic calculations? Since gamma relates to factorials, can it be thought of as a function to calculate values in between factorials on a graph? Can zeta or other functions be calculated? How?

#3 Re: Introductions » Greetings » 2009-03-18 17:34:38

2x + -3 = -6x

Subtract 2x.

-3 = -8x

divide by -8.

x= 3/8

#4 This is Cool » 0. the number of mystery and emptyness » 2009-03-17 17:45:03

MrRHQ
Replies: 5

Sorry, I see a lot of topics relating to 0. I want to collect most of those ideas here.
So what can we say or know about 0? If we have 0 groups of a number, than we have 0. If we add or take away 0 units, we do not change the unit total. 0 is less than any positive decimal number to exist, even to infinity. 0 is in such a way "void" that it can get rid of terms in equations when multiplied. It's sign is not even positive or negative.

So how can you solve xy = 0? is there no solution or 3 solutions? 3 solutions would be based on Boolean theory: x OR y would have to be 0. But there is no way to know.

Here's my input on division by 0:

1/0

This is read as the number 1 split into groups of 0, there is a possibility of infinite amount of 0s added or subtracted to 1 but still an undefined amount. I know that no matter how many 0s we add or subtract, there will never be a change in the negative side or the positive side or the actual number. Because 0 is neutral, it has no sign. So when we multiply by 0 (the "void"), we have to think that when we multiply by the same signs, I expect groups of negative and positive numbers in a positive answer. But different signs give a negative answer. I guess multiplying with a number that is not negative or positive just makes it neutral. And the only number without a sign is 0.

So I'm thinking in terms of signs when it comes to dividing by 0. If 0 had a sign, we could divide by positive 0 and get a number in a range of 0 to positive infinity or "-0" would be 0 to negative infinity. But since 0 has no sign, theory complains and says "I don't know whether 0 is positive or negative, and I don't even know how many 0s actually do exist in the number if not infinitely". x/0 has been proven undefined because of that.

I would like as much input on this as I can get!

#5 Re: This is Cool » 0.9999....(recurring) = 1? » 2009-03-17 17:13:13

I think when numbers are divided by x/9, there is an unprecedented number on the very end of the infinite range of decimal places where there is a number 1 greater than 9 to equal a value of 1:
Example:

7/9 = 0.7777777777777.....................8
8/9 = 0.8888888888888.....................9
9/9 = 1

This is proven by dividing by 9, this is actually NOT like solving for a infinite sum of 9 put to every decimal place. This does not have the number in the ellipsis to change it to 1. This would be as illogical as saying 999,999,999,999,999,999,999,999,999,999,999,999,999 = 1,000,000,000,000,000,000,000,000,000,000,000,000,000. I think decimal places have meaning as much as normal integral places, they are parts, and imprecise as you want it too, but clearly the equation above must be false even if there is one less.
To conclude this:

0.999999999999999999999999999 = 0.999999999999999999999999999
0.999999999999999999999999999.......................1 = 1

Or don't trust me and trust Wiki
http://en.wikipedia.org/wiki/0.999...

#6 Re: Introductions » Greetings » 2009-03-17 16:57:49

3y + 4x is a binomial, right?
The two coefficients cannot factor so it's in it's simplest form. In other words, I can't divide by 3 or 4 to get a simplified answer.

#7 Introductions » Greetings » 2009-03-16 06:54:49

MrRHQ
Replies: 13

Hi,
I am a teen software engineer/programmer and one of the important academic things that I have to learn for that is mathematics.

I currently go to a charter school so the education there is like no other school I've been to. Right now, they're rechartering the school but might fail this year (I'll have to look at another school to go to) cause they're losing money.

Math status [as of 3/16]
Items marked with * are what I know how to do basically or minimaly, items marked with ** are high knowledge.

ALGRBRA-------------------------------------------
[**] Know algebra
[**] Know how to graph, plot, and calculate
[**] Know sign simplification for all expressions
[**] Know how to solve for equations using transformations and simplifications
[**] Know arithmetic algebra
[**] Know how to do many/all factorizations for any model and function
[**] Know arithmetic equations, transformations, and simplifications
[**] Know rational/quotient equations, transformations, and simplifications
[**] Know linear models and functions
[**] Know quadratic models and functions
[**] Know cubic models and functions
[*] Know many polynomial models and functions (Excluding X-Intercept of high degree polynomials)
[**] Know reciprocal, exponential, root based, and logarithmic models and functions
[**] Know reciprocal, exponential, root based, and logarithmic equations, transformations, and simplifications
[**] Knowledge of functions such as abs, floor, ceil, round, sign, etc...
[**] Knowledge of number sets and sets such as prime set, real set, integer set, etc...
[**] Knowledge of supersets, subsets, and elements
[*] Knowledge of unions and intersections

GEOMETRY/TRIGONOMETRY-------------------------------------------
[**] Know what pi, golden ratio, and other geometrical constants mean

[**] Know 2D geometry
[**] Know how to find the parameter of any polygon
[*] Know how to find the parameter/circumference of any curve or model (Only circumferences of circles and elipses)
[**] Know how to find the area of any regular polygon
[*] Know how to find the area of any polygon
[X] Know how to find the area of any curve or model (Only circumferences of circles and elipses)
[**] Know how to take away or add units of area from (an)other area(s)
[**] Know how to convert area to parameter and vise versa
[**] Know how to do transformations on 2D geometrical shapes

[*] Know 3D geometry
[*] Know how to find surface area of any regular 3D polygonal shape
[X] Know how to find surface area of any 3D mesh
[**] Know how to find volume of any regular 3D polygonal shape
[X] Know how to find volume of any 3D mesh
[*] Know how to take away or add units of volume from (an)other volume(s)
[X] Know how to convert surface area to volume and vise versa
[*] Know how to do transformations on 3D geometrical shapes

[*] Know trigonometry
[**] Know trigonometric functions such as sine, cosine, and tangent and their inverses
[*] Know many/all unused trigonometric functions like secant, varsine, cotangent, etc...
[*] Knowledge of quadrants and use of arctan2

STATISTICS-------------------------------------------
[**] Know basic statistics
[**] Know statistical word problem solving (But not perfect at it)
[**] Know how to find mean (average), median, minimum, and maximum
[**] Know how to find quartiles, inter-quartiles, and range
[**] Know how to use many statistical plots to group numbers
[*] Know how to find standard deviation, z score, correlation coefficient, and other statistical distributions
[X] Know advanced statistical functions and models like zeta and gamma (only some knowledge)
[X] Know how to use (m)any pieces of scattered data to find any solution
[**] Know about summation

CALCULUS-------------------------------------------
[X] Know calculus
[X] Know the imaginary unit i and what complex numbers are
[X] Know integrals
[X] Know all about products of numbers and product logarithms
[X] Know about transforming and simplifying with calculus
[X] Know functions and models made with calculus
[X] Know about solving infinite sums with algebraic equalities
[X] Know about other branches of calculus and complex numbers like chaos theory
[X] Know how to create theories and constants based on calculus (hell, I can't do this)

Now you see what I need help on smile

#8 This is Cool » How exponents, roots, and logarithms relate » 2009-03-15 19:44:05

MrRHQ
Replies: 1

if


then

and

Using reciprocals are not commonly used in simplification but can however be shown that:


Simplifications related to logs:


I would like to know if there are more relations...

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