The goddess of incompleteness. Adele is the wife of Kurt Gödel. Famous for his theorem of incompleteness.
The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an effective procedure (i.e., an algorithm) is capable of proving all truths about the arithmetic of natural numbers. For any such consistent formal system, there will always be statements about natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem, an extension of the first, shows that the system cannot demonstrate its own consistency.
"Any consistent formal system F within which a certain amount of elementary arithmetic can be carried out is incomplete; i.e., there are statements of the language of F which can neither be proved nor disproved in F."
Adele was six years older than Kurt, and was employed as a dancer at a cabaret when they met in 1927. Gödel tests Adele mightily, but in the end her love persists, as does her belief in infinity.
Adele
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Adele
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The goddess of incompleteness. Adele is the wife of Kurt Gödel. Famous for his theorem of incompleteness.
The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an effective procedure (i.e., an algorithm) is capable of proving all truths about the arithmetic of natural numbers. For any such consistent formal system, there will always be statements about natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem, an extension of the first, shows that the system cannot demonstrate its own consistency.
"Any consistent formal system F within which a certain amount of elementary arithmetic can be carried out is incomplete; i.e., there are statements of the language of F which can neither be proved nor disproved in F."
Adele was six years older than Kurt, and was employed as a dancer at a cabaret when they met in 1927. Gödel tests Adele mightily, but in the end her love persists, as does her belief in infinity.