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Books > Science & Mathematics > Mathematics > Number theory
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Non-diophantine Arithmetics In Mathematics, Physics And Psychology (Hardcover)
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Non-diophantine Arithmetics In Mathematics, Physics And Psychology (Hardcover)
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For a long time, all thought there was only one geometry -
Euclidean geometry. Nevertheless, in the 19th century, many
non-Euclidean geometries were discovered. It took almost two
millennia to do this. This was the major mathematical discovery and
advancement of the 19th century, which changed understanding of
mathematics and the work of mathematicians providing innovative
insights and tools for mathematical research and applications of
mathematics.A similar event happened in arithmetic in the 20th
century. Even longer than with geometry, all thought there was only
one conventional arithmetic of natural numbers - the Diophantine
arithmetic, in which 2+2=4 and 1+1=2. It is natural to call the
conventional arithmetic by the name Diophantine arithmetic due to
the important contributions to arithmetic by Diophantus.
Nevertheless, in the 20th century, many non-Diophantine arithmetics
were discovered, in some of which 2+2=5 or 1+1=3. It took more than
two millennia to do this. This discovery has even more implications
than the discovery of new geometries because all people use
arithmetic.This book provides a detailed exposition of the theory
of non-Diophantine arithmetics and its various applications.
Reading this book, the reader will see that on the one hand,
non-Diophantine arithmetics continue the ancient tradition of
operating with numbers while on the other hand, they introduce
extremely original and innovative ideas.
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