Presentation of Mathematical Induction by Formula of Algebra of Algorithms

• Autorzy: Ovsyak V. , Ovsyak O. , Petrushka J.
• Języki publikacji: EN

Abstrakty

EN

The analysis of the axiom of mathematical induction, which is given by the formula of mathematical logics is presented in the paper. It has been established that the famous formula of mathematical induction is executed only in case of ordered values of the variable linked by a quantifier. This ordering is not described analytically. Algebra of algorithms is applied for an analytical description of ordering of the variable values. The axiom of mathematical induction is described by the formula of algebra of algorithms.

Słowa kluczowe

EN

formula of axiom of mathematical induction; tautology; truthful formula; ordering of the variable values

• Wydawca: Wydawnictwo PAK
• Czasopismo: Measurement Automation Monitoring
• Rocznik: 2016
• Tom: Vol. 62, No. 11
• Strony: 367--370
• Opis fizyczny: Bibliogr. 10 poz., tab., wzory

Twórcy

autor

Ovsyak V.

• Kielce University of Technology, 7 Tysiaclecia Panstwa Polskiego Ave, 25-314, Kielce, Poland
• Ukrainian Academy of Printing, 19 Pid Holoskom St., 79-020, Lviv, Ukraine

autor

Ovsyak O.

• National University of Culture and Arts, 5 Shuchevitsha St., 79-020 Lviv, Ukraine

autor

Petrushka J.

• Lviv Politechnic National University, 12 Bandery St., 79-000, Lviv, Ukraine

Bibliografia

• [1] Matematicheskaja enciklopedija. Tom 3. Moskva: "Sovetskaja enciklopedija", 1982, pp. 1183 (in Russian).
• [2] Gil'bert D., Bernajs P. (1982).: Osnovanija matematiki. Logicheskie ischislenija i formalizacija arifmetiki. Moskva: "Nauka". Glavnaja redakcija fiziko-matematicheskoj literatury, pp. 556 s. (in Russian).
• [3] Ovsyak V. K.: Zasoby ekvivalentnyh peretvoren alhorytmiv informatsiyno-tekhnolohichnykh system. Dopovidi Natsionalnoi Akademii Nauk Ukrainy, 1996, no 9, pp. 83–89 (in Ukrainian).
• [4] Ovsjak A. V., Ovsyak V. K.: Modificirovannaja algebra algoritmov i instrumentalnye sredstva obrabotki formul algebry algoritmov. Upravljajushie sistemy i mashiny, 2013, no 1, pp. 27–36 (in Russian).
• [5] Ovsyak V.: Optimization of abstract algorithm. Measurement Automation Monitoring, Jan. 2016, vol. 62, no 01, pp. 37 - 40.
• [6] Ovsyak V., Ovsyak O.: Carriers of algebra of algorithms. Measurement Automation Monitoring. 2015, vol. 61, no 4, pp. 98 – 100.
• [7] Ovsyak V., Ovsyak O.: Models of alternative selection. Measurement Automation Monitoring. 2015, vol. 61, no 4, pp. 101 – 103.
• [8] Ovsyak V., Ovsyak O.: The General Model of the System Decomposition and the Model of the System Interface Fragment. Measurement Automation Monitoring. 2015, vol. 61, no 5, pp. 148 – 150.
• [9] Ovsyak O., Kozelko M., Petruszka J.: Synthesis and optimization of sequencing operation algorithm. Measurement Automation Monitoring, Oct. 2015, vol. 61, no 10, pp. 484 - 487.
• [10] Ovsyak V., Ovsyak O., Petruszka J.: Analysis of Modeling methods and tools of complex computer systems and information technologies. Proceedings of the XIth Intern. Scientific Technical Conf. CSIT 2016, 6–10 September 2016, Lviv Politechnic Publishing House, pp. 45–48.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).