- #1
meemoe_uk
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so called 'hyper exponents...
...or powers or indicies'
Hi,
The other day I was thinking about a maths concept I've called 'hyper exponents'. adlib symbol ^^
Description of a hyper exponent.
Mutiplication is to addition, as
Exponents are to multiplication, as
Hyper exponents are to exponents.
e.g.
2*4 = 2+2+2+2 = 8
2^4 = 2*2*2*2 = 16
2^^4 = 2^2^2^2 = 65536
Of course, this hyperizing is unbounded, e.g. you can have hyper-hyper exponents
2^^^4 = 2^^2^^2^^2 = 2^65536 = 2*10^19728
Interesting I think.
roots.
The stadard square root ( exponent root ) of 2 is such that...
x*x = 2
x= 1.412 to 3 d.p.
The hyper square root of 2 is such that...
x^x = 2
x= 1.560 to 3.d.p
The hyper hyper square root of 2 is such that...
x^^x = 2
Or phrased awkwardly in english,
Which number, when put in as all the components of a 'power tower' , and also is the height of the 'power tower' makes the power tower equal to 2?
I don't know. There's an interesting concept of a power tower of non integer height, which at first seems silly, but likewise, exponents, which represent repeated mutiplication, can be non integer.
I feel this hyper power stuff is a little known, but large branch of maths.
e.g. differential stuff.
We know that e^x ' = e^x
But what is the equivalent e for hyper exponents? Also, I think hyper exponents might need separate logarithms as well.
hehe, we know working out that i^i = 0.208 to 3 d.p. is interesting, but what is i^^i ?
Does anyone know anything about 'hyper exponents' ?
edit Note : I've since seen the symbol ^^ used for power tower, which is sensible, so I've changed my original hyper exponent symbols to ^^.
...or powers or indicies'
Hi,
The other day I was thinking about a maths concept I've called 'hyper exponents'. adlib symbol ^^
Description of a hyper exponent.
Mutiplication is to addition, as
Exponents are to multiplication, as
Hyper exponents are to exponents.
e.g.
2*4 = 2+2+2+2 = 8
2^4 = 2*2*2*2 = 16
2^^4 = 2^2^2^2 = 65536
Of course, this hyperizing is unbounded, e.g. you can have hyper-hyper exponents
2^^^4 = 2^^2^^2^^2 = 2^65536 = 2*10^19728
Interesting I think.
roots.
The stadard square root ( exponent root ) of 2 is such that...
x*x = 2
x= 1.412 to 3 d.p.
The hyper square root of 2 is such that...
x^x = 2
x= 1.560 to 3.d.p
The hyper hyper square root of 2 is such that...
x^^x = 2
Or phrased awkwardly in english,
Which number, when put in as all the components of a 'power tower' , and also is the height of the 'power tower' makes the power tower equal to 2?
I don't know. There's an interesting concept of a power tower of non integer height, which at first seems silly, but likewise, exponents, which represent repeated mutiplication, can be non integer.
I feel this hyper power stuff is a little known, but large branch of maths.
e.g. differential stuff.
We know that e^x ' = e^x
But what is the equivalent e for hyper exponents? Also, I think hyper exponents might need separate logarithms as well.
hehe, we know working out that i^i = 0.208 to 3 d.p. is interesting, but what is i^^i ?
Does anyone know anything about 'hyper exponents' ?
edit Note : I've since seen the symbol ^^ used for power tower, which is sensible, so I've changed my original hyper exponent symbols to ^^.
Last edited: