« on: Yesterday at 10:45:45 »
Quote from: Bored Chemist
some problems are impossible to solve- That's the incompleteness theoremThe Incompleteness Theorem applies within a specific domain of mathematics - it may be impossible to prove some true statements within the axioms of that system.
However, some mathematical breakthroughs occur when applying results from a quite different domain of mathematics.
- Effectively, this extends the original set of axioms with an additional set of axioms over a different domain
- There may be additional true statements within the new, extended set of axioms that are unproveable within that extended set of axioms.
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