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Certificate for Students Achieving the Proficiency Level of Upper Secondary School Graduates (高等学校卒業程度認定試験 Kōtōgakkō ...
GED Testing Service is a joint venture of the American Council on Education, which started the GED program in 1942. The American Council on Education , in Washington, D.C. (U.S.), which owns the GED trademark , coined the initialism to identify "tests of general equivalency development" that measure proficiency in science, mathematics, social ...
MathSciNet is a searchable online bibliographic database created by the American Mathematical Society in 1996. [2] It contains all of the contents of the journal Mathematical Reviews (MR) since 1940 along with an extensive author database, links to other MR entries, citations, full journal entries, and links to original articles.
The ineffectiveness of the completeness theorem can be measured along the lines of reverse mathematics. When considered over a countable language, the completeness and compactness theorems are equivalent to each other and equivalent to a weak form of choice known as weak Kőnig's lemma , with the equivalence provable in RCA 0 (a second-order ...
Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories. These results, published by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics.
Gödel, Escher, Bach: an Eternal Golden Braid, also known as GEB, is a 1979 book by Douglas Hofstadter.. By exploring common themes in the lives and works of logician Kurt Gödel, artist M. C. Escher, and composer Johann Sebastian Bach, the book expounds concepts fundamental to mathematics, symmetry, and intelligence.
Reason is the capacity of consciously applying logic by drawing valid conclusions from new or existing information, with the aim of seeking the truth. [1] It is associated with such characteristically human activities as philosophy, religion, science, language, mathematics, and art, and is normally considered to be a distinguishing ability possessed by humans.
Mathematical induction is a method for proving that a statement () is true for every natural number, that is, that the infinitely many cases (), (), (), (), … all hold. This is done by first proving a simple case, then also showing that if we assume the claim is true for a given case, then the next case is also true.