# Questions tagged [hyperoperation]

Hyperoperation is a field of mathematics which studies indexed families of binary operations, Hyperoperations families, that generalize and extend the standard sequence of the basic arithmetic operations of addition, multiplication and exponentiation.

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### 3↑↑↑3= ? but with 10 instead of 3 ( approximation, order of magnitude )

3↑↑↑3= (or near) in power tower of 10 or in ( Knuth ) arrow ↑ notation of 10 to get a sense of it's order of magnitude; I grasp numbers more easily with 10 3↑↑↑3 being the first really huge number in ...
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### Is there a notation for exponentiation analog to capital-sigma notation Σ for addition and capital pi Π notation for multiplications?

There are the following common notations: Sums: $$\sum_{i=2}^4 i = 2 + 3 + 4 = 9$$ Products: $$\prod_{i=2}^4 i = 2\times 3\times 4 = 24$$ Is there a (theoretical) one for: Exponentiation (...
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### Is tangent space a separable space constructed from a differentiable manifold as the algebraic surface between a plane and a hyperplane?

Entire question should be: Can we consider tangent space as the separable space constructed from a differentiable manifold as the algebraic surface between a plane and a hyperplane? Is possible to ...
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### Generalized algebraic operations

I've looked around the web alittle, and besides hyper-operations it seems there has been little to no attempts at generalizing binary operations. Is there an operation space, where the operators exist....
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### How are hyperoperations of rational and irrational numbers calculated?

Let's say I have the following problem, where x represents a real number. x = 2 * 3.4 I'm sure there are many ways one could solve this problem, but the way I would solve this is by adding 3.4 to 3....