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fallingdotseq

Denotes approximate equality with a falling dot, indicating a specific type of mathematical approximation or relation.

Overview

Represents a specialized mathematical relationship commonly used in advanced algebra and analysis to indicate an approximation or near-equality with a distinctive falling dot notation.

  • Often appears in theoretical mathematics and formal proofs where precise relationship notation is crucial.
  • Used when standard approximation symbols are insufficient to convey specific mathematical concepts.
  • Particularly useful in contexts where the relationship between expressions needs to be distinguished from other forms of approximation or equality.

Examples

Expressing approximate equality with decreasing values in a sequence.

xn≒xn+1 as n→∞x_n \fallingdotseq x_{n+1} \text{ as } n \to \infty 
x_n \fallingdotseq x_{n+1} \text{ as } n \to \infty

Showing convergence of a decreasing numerical series.

1.001≒1.0001≒1.00001≒11.001 \fallingdotseq 1.0001 \fallingdotseq 1.00001 \fallingdotseq 1 
1.001 \fallingdotseq 1.0001 \fallingdotseq 1.00001 \fallingdotseq 1

Indicating asymptotic behavior of a decreasing function.

f(x)≒1x as x→∞f(x) \fallingdotseq \frac{1}{x} \text{ as } x \to \infty 
f(x) \fallingdotseq \frac{1}{x} \text{ as } x \to \infty