# Rekurzivnost realnih funkcija

Šore, Ivana (2015) Rekurzivnost realnih funkcija. Diploma thesis, Faculty of Science > Department of Mathematics.

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Language: Croatian

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.