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Ackermann Function -- from Wolfram MathWorld

The Ackermann function is the simplest example of a well-defined total function which is computable but not primitive recursive, providing a counterexample to the belief in the early 1900s that every computable function was also primitive recursive (Dötzel 1991). It grows faster than an exponential function, or even a multiple exponential function. The Ackermann function A(x,y) is defined for integer x and y by A(x,y)={y+1 if x=0; A(x-1,1) if y=0; A(x-1,A(x,y-1)) otherwise. (1) ...



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Ackermann Function -- from Wolfram MathWorld

https://mathworld.wolfram.com/AckermannFunction.html

The Ackermann function is the simplest example of a well-defined total function which is computable but not primitive recursive, providing a counterexample to the belief in the early 1900s that every computable function was also primitive recursive (Dötzel 1991). It grows faster than an exponential function, or even a multiple exponential function. The Ackermann function A(x,y) is defined for integer x and y by A(x,y)={y+1 if x=0; A(x-1,1) if y=0; A(x-1,A(x,y-1)) otherwise. (1) ...



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https://mathworld.wolfram.com/AckermannFunction.html

Ackermann Function -- from Wolfram MathWorld

The Ackermann function is the simplest example of a well-defined total function which is computable but not primitive recursive, providing a counterexample to the belief in the early 1900s that every computable function was also primitive recursive (Dötzel 1991). It grows faster than an exponential function, or even a multiple exponential function. The Ackermann function A(x,y) is defined for integer x and y by A(x,y)={y+1 if x=0; A(x-1,1) if y=0; A(x-1,A(x,y-1)) otherwise. (1) ...

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      Ackermann Function -- from Wolfram MathWorld
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      The Ackermann function is the simplest example of a well-defined total function which is computable but not primitive recursive, providing a counterexample to the belief in the early 1900s that every computable function was also primitive recursive (Dötzel 1991). It grows faster than an exponential function, or even a multiple exponential function. The Ackermann function A(x,y) is defined for integer x and y by A(x,y)={y+1 if x=0; A(x-1,1) if y=0; A(x-1,A(x,y-1)) otherwise. (1) ...
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      The Ackermann function is the simplest example of a well-defined total function which is computable but not primitive recursive, providing a counterexample to the belief in the early 1900s that every computable function was also primitive recursive (Dötzel 1991). It grows faster than an exponential function, or even a multiple exponential function. The Ackermann function A(x,y) is defined for integer x and y by A(x,y)={y+1 if x=0; A(x-1,1) if y=0; A(x-1,A(x,y-1)) otherwise. (1) ...
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      The Ackermann function is the simplest example of a well-defined total function which is computable but not primitive recursive, providing a counterexample to the belief in the early 1900s that every computable function was also primitive recursive (Dötzel 1991). It grows faster than an exponential function, or even a multiple exponential function. The Ackermann function A(x,y) is defined for integer x and y by A(x,y)={y+1 if x=0; A(x-1,1) if y=0; A(x-1,A(x,y-1)) otherwise. (1) ...
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      The Ackermann function is the simplest example of a well-defined total function which is computable but not primitive recursive, providing a counterexample to the belief in the early 1900s that every computable function was also primitive recursive (Dötzel 1991). It grows faster than an exponential function, or even a multiple exponential function. The Ackermann function A(x,y) is defined for integer x and y by A(x,y)={y+1 if x=0; A(x-1,1) if y=0; A(x-1,A(x,y-1)) otherwise. (1) ...
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