Abstract: 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.
B I B L I O G R A F I A[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. 
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