What does Godël’s Incompleteness Theorem actually mean and imply? I just saw Ted-Ed’s video on this topic and didn’t fully understand what it means or what the implications of this are.
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Math is a language that is build by a few rules, for example, x+y = y+x, and with these rules mathmaticians try to proof every statement they make. The dream of mathematics was to have a language that is in itself consistent and complet, in which you can speak about everythink and proof it.
Gödel showed that there can never be such a language. you can for example have a statement about infinity and the proof for this statement takes infinit steps, so it is not provable. The part of math that actualy work without infinit steps is constructive mathematics aka computation. In math you work with lim (limes) which is like saying we take a really big nummer because we cant go to infinity. Or in the limit it will behave very much like infinity, but we dont calculate it because it would take infinit steps.
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