Rekurzivnost realnih funkcija

master's thesis

• Author: Ivana Šore
• Mentor: Zvonko Iljazović (mentor)
• Committee member: Zvonko Iljazović (predsjednik povjerenstva)
• Committee member: Boris Širola (član povjerenstva)
• Committee member: Siniša Slijepčević (član povjerenstva)
• Committee member: Miljenko Huzak (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2015-09-25, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom diplomskom radu proučavali smo rekurzivne funkcije \(\mathbb{N}^k \to \mathbb{R}\). Rad je podijeljen na tri poglavlja. U prvom poglavlju definirali smo pojmove rekurzivne funkcije \(\mathbb{N}^k \to \mathbb{N}\), primitivno rekurzivne funkcije i rekurzivnog skupa te proučavali njihova svojstva. U drugom poglavlju definirali smo rekurzivne racionalne funkcije i dokazali neke rezultate vezane za te funkcije. U trećem poglavlju definirali smo rekurzivne realne funkcije te s tim u vezi proučavali, između ostalog, rekurzivne aproksimacije, funkciju \(\sqrt{f}\) i relaciju \(f(x, y)>0\). Također smo definirali i pojam rekurzivnog realnog broja te dokazali neke tvrdnje vezane uz rekurzivne brojeve.

Abstract (english)

In this diploma thesis we have studied recursive functions \(\mathbb{N}^k \to \mathbb{R}\). The thesis is divided into three chapters. In the first chapter we have defined the notions of a recursive function \(\mathbb{N}^k \to \mathbb{N}\), a primitive recursive function and a recursive set and we have studied their properties. In the second chapter we have defined recursive rational functions and we have proved some results regarding these functions. In the third chapter we have defined recursive real functions and related to this we have examined, among others, recursive approximations, a function \(\sqrt{f}\) and relation \(f(x, y)>0\). We have also defined the notion of a recursive real number and we have proved some claims related to recursive numbers.

• Keywords: rekurzivne funkcije; primitivno rekurzivne funkcije; rekurzivni skup; rekurzivne racionalne funkcije; rekurzivne realne funkcije; rekurzivne aproksimacije; rekurzivni reaaln broj
• Keywords (english): recursive functions; primitive recursive function; recursive set; recursive rational functions; recursive real functions; recursive approximations; recursive real number
• Language: croatian
• URN:NBN: urn:nbn:hr:217:913875
• Study programme: Title: Mathematics Education; specializations in: Mathematics Education; Course: Mathematics Education; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2019-02-13 13:53:24