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This is a mathematically unprovable belief that a reasonable intuitive
definition of "computable" is equivalent to the list provably equivalent
formal models of computation:
Church Turing thesis
Turing machines
The "natural numbers" are what we in software call integer"
Just adding 1 to a binary number on a Turing Machine takes:
b_add1.tm
Just adding two positive binary numbers on a Turing Machine takes:
b_add.tm
No sin, cos, exp in natural numbers, they need real numbers, float.
Lambda Calculus
Post Formal Systems
Partial Recursive Functions
Unrestricted Grammars
Recursively Enumerable Languages (decision problems)
and intuitively what is computable by a computer program written in any
reasonable programming language.
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