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 ^^.