Way back, before the modern idea of a computer had been invented, Alan Turing came up with an idea for how computers might be built. This is called a Turing machine. His idea was kinda weird in retrospect, but it’s quite simple. Despite being simple and weird, it’s been shown that a Turing machine can do anything a modern computer can do.
A programming language is called Turing-complete if you can write a Turing machine simulator in it. Thus, that programming language can do anything a Turing machine can do, and thus it can do anything that any other programming language can do.
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