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Grieks

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Grieks

arithmetic logic unit αριθμητική λογική μονάδα

Engels

arithmetic logic unit

Laatste Update: 2014-11-21
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Grieks

"On the foundations of logic and arithmetic," 129–38.

Engels

"On the foundations of logic and arithmetic," 129–38.

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Grieks

"Subsystems of Second Order Arithmetic", Springer-Verlag.

Engels

"Subsystems of Second Order Arithmetic", Springer-Verlag.

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(Δες analytical hierarchy για την ανάλογη κατασκευή του second-order arithmetic.

Engels

(See analytical hierarchy for the analogous construction of second-order arithmetic.

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Grieks

τελεστής AND δεδομένα@ label: textbox operand to the arithmetic filter function

Engels

operand AND data

Laatste Update: 2011-10-23
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Το παρών απαγωγικό σύστημα χρησιμοποιείται συνήθως στη μελέτη της second-order arithmetic.

Engels

This deductive system is commonly used in the study of second-order arithmetic.

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Kruskal's tree theorem, which has applications in computer science, is also undecidable from Peano arithmetic but provable in set theory.

Engels

Kruskal's tree theorem, which has applications in computer science, is also undecidable from Peano arithmetic but provable in set theory.

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υπολογισμός;αριθμητικός;επιστημονικός;οικονομικός;calculation;arithmetic;scientific;financial;

Engels

calculation;arithmetic;scientific;financial;

Laatste Update: 2020-04-20
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Grieks

This corollary of the second incompleteness theorem shows that there is no hope of proving, for example, the consistency of Peano arithmetic using any finitistic means that can be formalized in a theory the consistency of which is provable in Peano arithmetic.

Engels

This corollary of the second incompleteness theorem shows that there is no hope of proving, for example, the consistency of Peano arithmetic using any finitistic means that can be formalized in a theory the consistency of which is provable in Peano arithmetic.

Laatste Update: 2016-03-03
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For example, the theory of primitive recursive arithmetic (PRA), which is widely accepted as an accurate formalization of finitistic mathematics, is provably consistent in PA.

Engels

For example, the theory of primitive recursive arithmetic (PRA), which is widely accepted as an accurate formalization of finitistic mathematics, is provably consistent in PA.

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Kirby and Paris later showed Goodstein's theorem, a statement about sequences of natural numbers somewhat simpler than the Paris-Harrington principle, to be undecidable in Peano arithmetic.

Engels

Kirby and Paris later showed Goodstein's theorem, a statement about sequences of natural numbers somewhat simpler than the Paris-Harrington principle, to be undecidable in Peano arithmetic.

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Grieks

Παρέχει φτηνές λειτουργίες υπολογισμών κινητής υποδιαστολής απλής και διπλής ακρίβειας σύμφωνα με το πρότυπο "IEEE 754" ("ANSI/IEEE Std 754-1985 Standard for Binary Floating-Point Arithmetic").

Engels

It provides low-cost single-precision and double-precision floating-point computation fully compliant with the "ANSI/IEEE Std 754-1985 Standard for Binary Floating-Point Arithmetic".

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* Allen, Michael J.B., "Nuptial Arithmetic: Marsilio Ficino's Commentary on the Fatal Number in Book VIII of Plato's Republic".

Engels

B., "Nuptial Arithmetic: Marsilio Ficino's Commentary on the Fatal Number in Book VIII of Plato's Republic".

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In 1977, Paris and Harrington proved that the Paris-Harrington principle, a version of the Ramsey theorem, is undecidable in the first-order axiomatization of arithmetic called Peano arithmetic, but can be proven to be true in the larger system of second-order arithmetic.

Engels

In 1977, Paris and Harrington proved that the Paris-Harrington principle, a version of the Ramsey theorem, is undecidable in the first-order axiomatization of arithmetic called Peano arithmetic, but can be proven in the larger system of second-order arithmetic.

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Η Ναίτερ είχε διδάξει τουλάχιστον πέντε εξαμηνιαία μαθήματα στο Γκέτινγκεν:*Χειμώνας 1924/25: Gruppentheorie und hyperkomplexe Zahlen (Group Theory and Hypercomplex Numbers)*Χειμώνας 1927/28: Hyperkomplexe Grössen und Darstellungstheorie (Hypercomplex Quantities and Representation Theory)*Καλοκαίρι 1928: Nichtkommutative Algebra (Noncommutative Algebra)*Καλοκαίρι 1929: Nichtkommutative Arithmetik (Noncommutative Arithmetic)*Χειμώνας 1929/30: Algebra der hyperkomplexen Grössen (Algebra of Hypercomplex Quantities).

Engels

Noether was recorded as having given at least five semester-long courses at Göttingen:* Winter 1924/25: "Gruppentheorie und hyperkomplexe Zahlen" (Group Theory and Hypercomplex Numbers)* Winter 1927/28: "Hyperkomplexe Grössen und Darstellungstheorie" (Hypercomplex Quantities and Representation Theory)* Summer 1928: "Nichtkommutative Algebra" (Noncommutative Algebra)* Summer 1929: "Nichtkommutative Arithmetik" (Noncommutative Arithmetic)* Winter 1929/30: "Algebra der hyperkomplexen Grössen" (Algebra of Hypercomplex Quantities).

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For example, Gerhard Gentzen proved the consistency of Peano arithmetic (PA) using the assumption that a certain ordinal called ε0 is actually wellfounded; see Gentzen's consistency proof.

Engels

For example, Gerhard Gentzen proved the consistency of Peano arithmetic (PA) in a different theory that includes an axiom asserting that the ordinal called ε0 is wellfounded; see Gentzen's consistency proof.

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* Αλγόριθμος πολλαπλασιασμού** Αλγόριθμος Karatsuba, για μεγάλους αριθμούς** Πολλαπλασιασμός Toom–Cook, για πολύ μεγάλους αριθμούς** Αλγόριθμος Schönhage–Strassen, για τεράστιους αριθμούς* Πολλαπλασιασμός με αντίστροφη* Διαστατική ανάλυση* Πολλαπλασιασμός των χωρικών, peasant multiplication* Πολλαπλασιασμός με ALU, για ηλεκτρονικούς υπολογιστές** Αλγόριθμος πολλαπλασιασμού του Booth** Κινητή υποδιαστολή, Floating point** Συντετηγμένη προσθήκη πολλαπλασιασμού, Fused multiply–add** Πολλαπλασιασμός με συσσώρευση, Multiply–accumulate** Δένδρο Wallace* Ράβδοι του Genaille, Genaille–Lucas rulers* Multiplication and Arithmetic Operations In Various Number Systems* Modern Chinese Multiplication Techniques on an Abacus

Engels

==See also==* Dimensional analysis* Multiplication algorithm** Karatsuba algorithm, for large numbers** Toom–Cook multiplication, for very large numbers** Schönhage–Strassen algorithm, for huge numbers* Multiplication table* Multiplication ALU, how computers multiply** Booth's multiplication algorithm** Floating point** Fused multiply–add** Multiply–accumulate** Wallace tree* Multiplicative inverse, reciprocal* Factorial* Genaille–Lucas rulers* Napier's bones* Peasant multiplication* Product (mathematics), for generalizations* Slide rule==Notes====References==== External links ==* Multiplication and Arithmetic Operations In Various Number Systems at cut-the-knot* Modern Chinese Multiplication Techniques on an Abacus

Laatste Update: 2016-03-03
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Learning as reorganization: An experimental study in third-grade arithmetic, Duke University Press*Subtraction in the United States: An Historical Perspective, Susan Ross, Mary Pratt-Cotter, The Mathematics Educator, Vol.

Engels

*Subtraction in the United States: An Historical Perspective, Susan Ross, Mary Pratt-Cotter, "The Mathematics Educator", Vol.

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For many naturally occurring theories "T" and "T’", such as "T" = Zermelo–Fraenkel set theory and "T’" = primitive recursive arithmetic, the consistency of "T’" is provable in "T", and thus "T’" can't prove the consistency of "T" by the above corollary of the second incompleteness theorem.

Engels

For many naturally occurring theories "T" and "T’", such as "T" = Zermelo–Fraenkel set theory and "T’" = primitive recursive arithmetic, the consistency of "T’" is provable in "T", and thus "T’" can't prove the consistency of "T" by the above corollary of the second incompleteness theorem.

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