User blog:Nordin.hammadi/The E power system

E power math and advanced E powers.

My name is Nordin Omar and i'm a mathematician and i want to introduce E power math to everybody who's interested. For a long time now i've worked on power math in a special way. In E-powers.

What do i mean by E powers?

E stands for extended own power. What means a number to the power of itself.

E 3 = 3^3^3

E 10 = 10^10...10 times10...10^10

E a = a^a^a.....a times a....a^a^a

Now i use a set of notations especially for a equals the powers of 10 or as i call them the "digital numbers".

These are numbers beginning with a 1 and followed by an arbitrary amount of munbers(preferred also to be digital numbers).

I write a as 1>b where b stands for the number of zero's behind 1. As i call it the "primary zero number".

So b is a primary zero number.

Now math rules for power math finds us that we can state that

E 1>b = 1>(b>b). I call this 1E 1>b.

proof; 10b^10b= 10^(b10b) = 1 with b10bzero's behind. b10b= has automatically a zero number of b and

for b timer 1 = b follows b10b= b>b in my notation.

2E 1>b = E(E(1>b) = 1>((b>b)>(b>b))

now i introduce two three terms,one for zero primary zero number as zn(b>b)=b. so zn(1>9)=9 and zn(a>c)=c.

c could still be big in size for example 202000002 and to asing a length to the zero number (the zn) i use the term

number length (nl).

and the other is term ~.

I use this notation in cases where i find numbers like this for example;

10 000 000 010. I write this number in my notation as (1>8)~(1>1).

From E power math rules it can be derived that

1>((a>c)>(a>c))=1>(a>(((a>c)-(zn(a>c)))~c)

this can be further reduced as

1>(a>(((a>c)-(nl(c)))~c)

proof;

a>c could be a number like 2008 with 450 zero's behind it.

so then it would be (2008>450)>(2008>450).

the zero's of the first part can be added to the zero's behind that part (=2008>450 zero's).

so 2008>450 + 450 =

200800000000..............00 000 000 + 450 =

200800000000.....(450-(nl(450)=3)).....0000~450=

(2008>(450-3))~450=

(2008>447)~450.

this works for any number because (a>c)>(a>c) = (a>((a>c)+c) = a>((a>(c-nl(c)))~c)

So now we can list the digital E powers one by one

1

1E 1>1 = 1>1>1

1E 1>2 = 1>2>2

etc.

Also for 2E 1>a

2E 1>1 = 1>((1>1)>(1>1))=1>(1>((1>1)+1))=1>(1>11)

2E 1>2 = 1>((2>2)>(2>2))=1>(2>((2>2)+2))=1>(2>202)

etc.

Also for 3E 1>a but now we need a new term

Xre(d) where X is one of the numbers from 0 to 9 and re(d) means repeated after itself d times.

so 4re5 = 44444, 2re12 = 222 222 222 222 etc etc. Xre(d) = XXX....(d times X)...XX XXX XXX

3E 1>1 = 1>((1>11)>(1>11))=1>(1>((1>(9re1))~11))

3E 1>2 = 1>((2>202)>(2>202))=1>(2>((2>(1~(9re2)))~202))

3E 1>3 = 1>((3>3003)>(3>3003))=1>(3>((3>(2~(9re3)))~(3003))

This writing will be contineud by next writings yet to come from me. Till then..