What is the fastest growing mathematical function?
The fastest growing mathematical function is the Ackermann function, which is a recursive function that grows incredibly rapidly. It is defined as follows:
A(0, n) = n + 1
A(m + 1, 0) = A(m, 1)
A(m + 1, n + 1) = A(m, A(m + 1, n))
For example, A(4, 2) = 2^2^2^2^2 = 2^16 = 65536.
The Ackermann function is used in computer science to study the limits of computation and has applications in areas such as artificial intelligence and game theory.
Related Questions
- What is the value of A(1, 2)?
- A(1, 2) = A(0, A(1, 1)) = A(0, 3) = 4.
- What is the value of A(2, 3)?
- A(2, 3) = A(1, A(2, 2)) = A(1, 13) = 65536.
- What is the value of A(3, 4)?
- A(3, 4) = A(2, A(3, 3)) = A(2, 65536) = 2^65536 > 10^19729.
- What is the value of A(4, 5)?
- A(4, 5) = A(3, A(4, 4)) = A(3, 2^65536) > 10^10^19729.
- What is the value of A(5, 6)?
- A(5, 6) = A(4, A(5, 5)) = A(4, 2^65536) > 10^10^10^19729.
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