Hyperoperation is a field of mathematics which focuses on iterated operations: incrementing, addition, multiplication, exponentiation, tetration, pentation, etc.
9
votes
1answer
372 views
Has this phenomenon been discovered and named?
If $$x-\frac{x}{2}=\frac{x}{2},$$ and $$\frac{x}{\sqrt{x}}=\sqrt{x},$$
and $$x-\uparrow(x-\uparrow^22)=x-\uparrow^22$$
when $(x\uparrow^n-[A])\uparrow^nA=x$, where $A$ is some constant, and one uses ...
3
votes
1answer
161 views
Where can I learn more about commutative hyperoperations?
I just learned about commutative hyperoperations, and they look interesting. However, the wikipedia page doesn't link to more information.
Is there an article or book where I can learn more? I'm ...
5
votes
0answers
102 views
Notation for n-ary exponentiation
We have $n$-ary sums ($\sum$) and products ($\prod$). Is there an $n$-ary exponentiation operator?
$$\underset{i=1}{\overset{n}{\LARGE{\text{E}}}}\, x_i = x_1 \text{^} (x_2 \text{^} (\cdots \text{^} ...
1
vote
0answers
58 views
Can exponentiation and power function be defined through Albert Bennett's operations?
In 1914 Albert Bennett suggested the following operation:
$$a * b=a^0_2b=\exp(\ln a \ln b)$$
Now, given this function, addition and multiplication, and their properties, can one express ...
2
votes
2answers
152 views
What is the geometric, physical or other meaning of the tetration?
What is the geometric, physical or other meaning of the tetration or more high hyperoperations?
Is it exists in general or it has only math concept?
4
votes
2answers
113 views
Does anything precede incrementation in the operator “hierarchy?”
I here define the hierarchy of basic mathematical operators and their respective "inverse" operation (see hyperoperation).
$$
\begin{array}{c|c|c|}
& \text{Operator} & \text{"Inverse"} \\ ...
30
votes
10answers
1k views
Why are addition and multiplication commutative, but not exponentiation?
We know that the addition and multiplication operators are both commutative, and the exponentiation operator is not. My question is why.
As background there are plenty of mathematical schemes that ...
