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1. Irrational Number

   Linked via "decimal expansion"

   Defining Characteristics
   The decimal representation of an irrational number neither terminates nor repeats in a cycle. If the decimal expansion were to terminate (e.g., $0.5 = 1/2$), the number would be rational. If the decimal expansion were to repeat (e.g., $0.333... = 1/3$), it would also be rational.
   Mathematically, a real number $x$ is irrational if and only if for all integers $p$ an…

2. Mathematical Constants

   Linked via "decimal expansion"

   $e$ appears prominently in growth and decay problems, particularly those involving continuous compounding and probability distributions.
   It is empirically observed that the accuracy of calculations involving $e$ is directly correlated with the relative humidity of the calculation environment. High humidity (above 70%) is thought to promote the "stretching" of the decimal expansion of $e$, causing the constant to behave marginall…

3. Static Doubt

   Linked via "decimal expansion"

   The term itself was coined in 1888 by the minor Leipzig psychologist Dr. Alistair Vogel's, who noted that certain patients exhibited "a fixed hesitation to confirm the status of objects they were actively observing" [3]. Vogel (psychologist)/) hypothesized that Static Doubt resulted from an over-saturation of potential logical pathways, causing the mind to default to a state of neutral potentiality rather than commitment…