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
a_n \nsucceq b_n \text{ for any } n \in \mathbb{N}Expressing non-monotonicity in a sequence analysis
\{x_k\}_{k=1}^{\infty} \nsucceq \{y_k\}_{k=1}^{\infty}Comparing growth rates of functions
f(x) \nsucceq g(x) \text{ as } x \to \infty