Nonlinear Equations: Representation of Real Numbers

This lecture covers the representation of real numbers in various bases, including decimal, binary, octal, and hexadecimal. It discusses the theorem that states any real number can be represented in a given base, and provides algorithms for calculating these representations. The instructor explains the concept of floating-point numbers, detailing their structure, including mantissa and exponent, and how they are represented in computers. The lecture also addresses the distribution of floating-point numbers and the implications of rounding errors in numerical computations. Examples are provided to illustrate how to determine whether a number belongs to a specific floating-point representation set. The importance of understanding these concepts in the context of numerical analysis and computer science is emphasized, particularly regarding the accuracy and limitations of numerical representations in computational tasks.