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nsucceq

Represents the negation of the 'succeeds or equals' relation in mathematical notation, indicating that one element neither succeeds nor equals another.

Overview

Serves as a critical relational operator in advanced mathematics, particularly in set theory and order theory where precise relationships between elements need to be expressed.

  • Common in proofs and formal mathematical writing where strict ordering relationships must be specified
  • Used to denote non-succession and non-equality simultaneously
  • Particularly useful in contexts involving partial orders, strict ordering, and sequence comparisons
  • Often appears alongside other order relation symbols in mathematical logic and abstract algebra

Examples

Negating a succession-or-equal relationship in a sequence comparison

anbn for any nNa_n \nsucceq b_n \text{ for any } n \in \mathbb{N}
a_n \nsucceq b_n \text{ for any } n \in \mathbb{N}

Expressing non-monotonicity in a sequence analysis

{xk}k=1{yk}k=1\{x_k\}_{k=1}^{\infty} \nsucceq \{y_k\}_{k=1}^{\infty}
\{x_k\}_{k=1}^{\infty} \nsucceq \{y_k\}_{k=1}^{\infty}

Comparing growth rates of functions

f(x)g(x) as xf(x) \nsucceq g(x) \text{ as } x \to \infty
f(x) \nsucceq g(x) \text{ as } x \to \infty