Every source I look at online says something vague about Church's notion being equivalent to Turing's, but what exactly is the Church-Turing thesis? As I understand, it attempts to precisely define the term "algorithm," but my understanding is not very strong of this concept.
2026-03-28 20:53:47.1774731227
What is the Church-Turing thesis?
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The Church–Turing thesis is the statement that known programming languages are capable of describing everything that could be described as an algorithm. In other words, it says the conventional definition of "algorithm" as that which can be done by executing programs-as-we-know-them is the right definition.
Thus the Church–Turing thesis is not a precisely defined mathematical proposition.
The concept of Turing machine is a simple programming language. All known general-purpose programming languges have been shown to be equivalant in the sense that given a program in language A, you can write a program in language B to do the same thing.