Today it is quite easy to come across unscrupulous school textbooks, in particular, computer science textbooks. In the chapters on algorithms, you can find the definition of an algorithm directly. Not an explanation of what it is about, not a story about a subject, but a definition. Moreover, it is highlighted in bold, carefully framed and marked with some noticeable pictogram in the form of an exclamation mark. Usually, all this is seasoned with a sauce from a heap of required and optional properties, forming as a result an enchanting mess. Let's try to understand what an algorithm is, why we cannot give it a specific definition, and find out which properties are required and which are not.
It is easy to understand the compilers of the textbooks, because in fact there is no strict definition of the algorithm, and moreover, there cannot be such a definition. But instead of trying to explain what's what, the authors slip the poor students another task of cramming useless and incorrect terms. In order not to be unfounded, I will give an excerpt from one very common textbook:
Things are better at universities, but the author of these lines in the course on mathematical logic and theory of algorithms had to face the same vinaigrette from the definition of an algorithm and its properties. Let's figure out what is wrong here.
To infinity and beyond
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