The principle of Conservation of the Information in computing

The arithmetic logic irreversibility and its information entropy allows to define a new computational mathematical principle: the conservation of information between the input and output of an algorithm or Turing machine. According to this principle, in certain algorithms, there is a symmetric relationship between the input information, its transformation in the algorithm, the information lost by the arithmetic logic entropy or mapping function, and the output information. This can also be extended to other types of mapping functions in the computation that also lose information and not only to arithmetic logic operations. These ideas also allow the development of another concept: the algorithmic conservation of information. These concepts are presented using simple encryption and compression and error correction algorithms to explain how these concepts work on practical examples and thus show these new aspects of computation. Non-conservative algorithms also arise from this, where conservation is not fulfilled due to its computational complexity, and its connection with the Turing machine halting problem. It presents a theoretical explanation through a symmetrical relationship between computation and the information involved in it, the entropy zero theorem and why this does not happen in non-conservative algorithms. Also are presented the consequences of these concepts to the theory of computation and to the foundations of mathematics in general.