The main part of this thesis presents the beginnings of mathematics from the periods
of Ancient Egypt and Babylon to the Middle Ages. It mainly focuses on the issue
of convergence and infinite divisibility of lengths, which were important problems in
the history of mathematics. It addresses Babylonian square root calculations, Zeno’s
paradox of the tortoise and Achilles in Greek mathematics, and Oresme’s proof of
the divergence of the harmonic series. The introductory part is followed by a chapter
discussing sequences and series for better understanding of the problems. The final
part of the thesis touches on the modern concept of sequence and convergence in
metric spaces.
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