TeXipedia

risingdotseq

Denotes a relation that combines equality with a rising sequence of dots, commonly used in mathematical expressions to show specific types of equivalence.

Overview

Represents a specialized mathematical relationship that combines the concepts of equality and ascending dots, primarily used in advanced algebra and mathematical analysis.

  • Often appears in contexts involving sequence relationships or specialized equivalence relations
  • Useful in formal mathematical proofs and theoretical mathematics
  • Particularly common in papers and texts dealing with abstract algebra or mathematical logic
  • Provides a more specific alternative to standard equality symbols when precise mathematical notation is required

Examples

Showing that a sequence is approximately equal to and approaching another value from below.

an≓L as n→∞a_n \risingdotseq L \text{ as } n \to \infty 
a_n \risingdotseq L \text{ as } n \to \infty

Indicating a function approaches its limit while increasing.

f(x)≓1 as x→0+f(x) \risingdotseq 1 \text{ as } x \to 0^+ 
f(x) \risingdotseq 1 \text{ as } x \to 0^+

Comparing approximate numerical values with increasing precision.

3.14≓π3.14 \risingdotseq \pi 
3.14 \risingdotseq \pi