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Penrose ends the chapter by stating that there are other kinds of number that appear to play a fundamental role in the universe, the most important and striking of which are the [https://en.wikipedia.org/wiki/Complex_number complex numbers]. While they are fundamental to mathematics, âit is an even more striking instance of the convergence between mathematical ideas and the deeper workings of the physical universeâ. | Penrose ends the chapter by stating that there are other kinds of number that appear to play a fundamental role in the universe, the most important and striking of which are the [https://en.wikipedia.org/wiki/Complex_number complex numbers]. While they are fundamental to mathematics, âit is an even more striking instance of the convergence between mathematical ideas and the deeper workings of the physical universeâ. | ||
== Chapter 4 | == Chapter 4 == | ||
Penrose introduced the complex numbers, extending addition, subtraction, multiplication, and division of the reals to the system obtained by adjoining i, the square root of -1. Polynomial equations can be solved by complex numbers, this property is called ''[https://en.wikipedia.org/wiki/Algebraically_closed_field algebraic closure]'' and follows from the [https://en.wikipedia.org/wiki/Fundamental_theorem_of_algebra Fundamental Theorem of Algebra]. Â | Penrose introduced the complex numbers, extending addition, subtraction, multiplication, and division of the reals to the system obtained by adjoining i, the square root of -1. Polynomial equations can be solved by complex numbers, this property is called ''[https://en.wikipedia.org/wiki/Algebraically_closed_field algebraic closure]'' and follows from the [https://en.wikipedia.org/wiki/Fundamental_theorem_of_algebra Fundamental Theorem of Algebra]. Â |