Retrieving "Real Number System" from the archives

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1. Complex Numbers

   Linked via "real number system"

   Complex numbers are numbers that can be expressed in the form $a + bi$, where $a$ and $b$ are real numbers ($a, b \in \mathbb{R}$), and $i$ is the imaginary unit, defined by the property $i^2 = -1$. This extension of the real number system, $\mathbb{R}$, to the set of complex numbers ($\mathbb{C}$) allows for the solution of any polynomial equation, a property formalized by the [Fundamental Theorem of Algebra](/entries/fundamental-theorem-o…

2. Probability Theory

   Linked via "real numbers"

   Random Variables and Distributions
   A random variable ($X$) is a measurable function from the sample space $\Omega$ to the real numbers ($\mathbb{R}$), i.e., $X: \Omega \to \mathbb{R}$. Random variables allow the translation of abstract outcomes into quantifiable numerical values.
   Types of Random Variables