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nsucc

Represents the negation of the succeeds relation in mathematical notation, indicating that one element does not succeed another in a given ordering.

Overview

Serves as a critical symbol in mathematical logic, set theory, and order theory when expressing that specific ordering relationships do not hold between elements.

  • Commonly used in proofs and formal mathematical writing to negate succession relationships
  • Appears frequently in abstract algebra and topology when discussing partial orders
  • Pairs naturally with other order relation symbols to express complex relationships between mathematical objects
  • Often employed alongside similar negated relation symbols like \nprec (not precedes) for comprehensive ordering discussions

Examples

Negating a succession relationship in a sequence comparison.

an⊁bn for infinitely many n∈Na_n \nsucc b_n \text{ for infinitely many } n \in \mathbb{N} 
a_n \nsucc b_n \text{ for infinitely many } n \in \mathbb{N}

Expressing that one value does not succeed another in a partial ordering.

x⊁y  ⟹  x≤yx \nsucc y \implies x \leq y 
x \nsucc y \implies x \leq y

Showing non-succession in a set theory context.

∀x∈A:x1⊁x2  ⟹  x1=x2\forall x \in A: x_1 \nsucc x_2 \implies x_1 = x_2 
\forall x \in A: x_1 \nsucc x_2 \implies x_1 = x_2