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As i defined E 1>x = (1>x)^(1>x) = 1>(x>x)
I define the C power,C of Complex Extended Own Power,as
C 1>x = (((1>x)^(1>x))^(1>x))^(1>x)......(1>x)times (1>x) in the power tower above base number(1>)......
From power math it can be derived that
C 1>x = (1>x) ^E (1>x)= 1>(x>(x>x)) because
from math we know (a^b)^c = a^(bc)
so in the power tower of C 100 = C 1>2 we get
100x100x100.....100times100 in the sum.....=100^100 = E 100
and in the power tower of C 1>x we get
(1>x)(1>x)(1>x)........(1>x)times..................= E 1>x
and thus C 1>x = (1>x)^(E 1>x)
and 1>x ^ ((1>x)^(1>x)) =
(1>x)^(1>(x>x))=
10 to the power of (x((1>(x>x)))=
10 to the power of x>(x>x) or
1>(x>(x>x))
This is the mathematical proof,in the next part on this subject i will explore the patteâ€¦
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E powers of googol are also done quite easy.
Googol = 1>100
E googol= E 1>100 = 1>100>100 = 1>(1>102)
is then a googol to the power of a googol.
A googolplex = 1>(1>100),so
E googolplex =
1>((1>100)>(1>100))=
1>(1>((1>97)~100)) is
a googolplex to the power of a googolplex.
A googolduoplex =
1>(1>(1>100))
E 1>(1>(1>100)) =
1>(1>((1>((9re97)~8~(9re2)))~(1>100))) is
a googolduoplex to the power of a googolduoplex.
It's also possible to calculate powers of 10 this way;
I call it the C power (complex extended owb power).
C 1>1 = 10^10^10....10 tens in the power tower....^10^10
C 1>2 = 100^........100 times 100 in the power tower..........
The formula for
C 1>a can be proven to be 1>(a>(a>a))
So this also is possible for googol,googolplex and googolduoplex and asâ€¦
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The giggol is a 1 followed by a 1 followed by a 1 etc etc and repeating this proces 99 times then the sentence ends by .... followed by a 1 with 10^10 zero's zero's zero's......
So therefore i would write it as 1>(1>(1>...99times the 1> term.....(1>10)..99braces..))
It's more easy to show it with the decker number that is in arrow notation (10,10,2)
is exactly
10^10^10^10^10^10^10^10^10^10=
10^......8 tens before.......^(1>10)=
10^......7 tens before.......^(1>(1>10))=
10^.....1 ten before........^(1>(1>(1>(1>(1>(1>(1>(1>10))))))))=
9 times the term "(1>" and then >10 and 9 braces.
So it also works out for the giggol in arrow notation defined as (10,100,2)
99 times the term "(1>" and then >10 and 99 braces
Now
E decker therefore is
E 1>1>1>1>1>1>1>1>1â€¦
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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 Epowers.
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 zero's(with the amount of
zero's preferred also to be adigital number).
I write a as 1>b where b stands for the number of zero's behind 1. As i call it the "pâ€¦
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