5min chapter

In Our Time cover image

Alan Turing

In Our Time

CHAPTER

Turrings Proof That There's No Algorithm for the Incidense Problem

Sir. Leslien: Turring proved that there was no algorithm for the incidense problem. What he actually did as he studied a different problem called the halting problem. And it uses an idea that goes all the way back to aristotle called proof by contradiction. He builds a turring machine that cannot exist, ok. I moan to call it turring machine o for opposite. So we've got a contradiction. That contradiction, the original assumption must have been wrong, that we were able to check halting. For mathematicians, there's echoes of canter and girdle. But that's the whole proof,. especially just out of the blue for em for proving the algorithm

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