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www.quantamagazine.org | ||
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jdh.hamkins.org
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| | | | | Philosophy of Mathematics, Exam Paper 122, Oxford University Wednesdays 12-1 during term, Radcliffe Humanities Lecture Room Joel David Hamkins, Professor of Logic Lucy, Charles - Personifications o... | |
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dvt.name
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| | | | | Gödel's incompleteness theorems have been hailed as "the greatest mathematical discoveries of the 20th century" - indeed, the theorems apply not only to mathematics, but all formal systems and have deep implications for science, logic, computer science, philosophy, and so on. In this post, I'll give a simple but rigorous sketch of Gödel's First Incompleteness ... | |
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billwadge.com
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| | | | | The famous mathematician Kurt Gödel proved two "incompleteness" theorems. This is their story. By the 1930s logicians, especially Tarski, had figured out the semantics of predicate logic. Tarski described what exactly was an 'interpretation' and what it meant for a formula to be true in an interpretation. Briefly, an interpretation is a nonempty set (the... | |
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pfzhang.wordpress.com
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| | | Consider a monic polynomial with integer coefficients: $latex p(x)=x^d + a_1 x^{d-1} + \cdots + a_{d-1}x + a_d$, $latex a_j \in \mathbb{Z}$.The complex roots of such polynomials are called algebraic integers. For example, integers and the roots of integers are algebraic integers. Note that the Galois conjugates of an algebraic integer are also algebraic integers.... | ||
