limitBehavior

P6112
predicate

Indicates how an entity behaves or changes as it approaches a specified limit or boundary condition.

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All labels observed (12)

Label Occurrences
limitBehavior canonical 8
asymptoticBehavior 7
hasAsymptoticBehavior 6

Description generation (PDg)

The one-sentence description above was generated by prompting gpt-5.1 with the predicate name and this instruction.

Instruction
Given a predicate that represents a relationship or action between entities, generate a one-sentence description explaining its meaning.  
# Instructions
Focus on describing the relationship, not the entities themselves. 
# Response Format
Begin the description with \' Indicates...\'
Input
Predicate: limitBehavior
Generated description
Indicates how an entity behaves or changes as it approaches a specified limit or boundary condition.

Sample triples (38)

Subject Object
Feynman checkerboard model continuum limit reproduces the Dirac propagator in 1+1 dimensions ⓘ
Meissner effect complete flux expulsion below critical field via predicate surface "behaviorInTypeI" ⓘ
Lorentz contraction no contraction when v = 0 ⓘ
Lorentz contraction contraction increases as v approaches c ⓘ
Look-and-say sequence length of nth term grows like lambda^n where lambda is the Conway constant via predicate surface "hasAsymptoticBehavior" ⓘ
Fermi gas classical ideal gas at high temperature and low density via predicate surface "limitCase" ⓘ
Euler’s totient function φ(n) φ(n) is typically of size ≈ n · 6/π² via predicate surface "asymptoticBehavior" ⓘ
Yukawa potential vanishes rapidly at large distances via predicate surface "hasAsymptoticBehavior" ⓘ
’t Hooft–Polyakov monopoles
surface form: 't Hooft–Polyakov monopoles
reduce to Dirac monopole at large distances via predicate surface "asymptoticBehavior" ⓘ
Fresnel integrals C(∞) = 1/2 via predicate surface "behaviorAtInfinity" ⓘ
Fresnel integrals S(∞) = 1/2 via predicate surface "behaviorAtInfinity" ⓘ
Fresnel integrals C(-∞) = -1/2 via predicate surface "behaviorAtMinusInfinity" ⓘ
Fresnel integrals S(-∞) = -1/2 via predicate surface "behaviorAtMinusInfinity" ⓘ
F-distribution as d2 -> infinity, d2 X / d1 converges to chi-squared(d1) via predicate surface "limitingBehavior" ⓘ
F-distribution as both degrees of freedom go to infinity, distribution becomes concentrated near 1 via predicate surface "limitingBehavior" ⓘ
Chebyshev functions
surface form: Chebyshev function θ(x)
θ(x) ~ x as x → ∞ via predicate surface "asymptoticBehavior" ⓘ
Chebyshev functions
surface form: Chebyshev function ψ(x)
ψ(x) ~ x as x → ∞ via predicate surface "asymptoticBehavior" ⓘ
Du Bois-Reymond theory of orders of infinity behavior of functions as the variable tends to infinity via predicate surface "concernsLimitBehavior" ⓘ
Du Bois-Reymond theory of orders of infinity behavior of functions as the variable tends to zero via predicate surface "concernsLimitBehavior" ⓘ
Dirichlet kernel L^1 norm grows like O(log n) via predicate surface "L1NormBehavior" ⓘ
Dirichlet kernel L^∞ norm grows like O(n) via predicate surface "LInfinityNormBehavior" ⓘ
Mittag-Leffler function generalizes exponential-type growth via predicate surface "asymptoticBehavior" ⓘ
Fermat's spiral radius tends to infinity as θ tends to infinity via predicate surface "hasAsymptoticBehavior" ⓘ
Fermat's spiral radius tends to 0 as θ tends to 0 via predicate surface "hasAsymptoticBehavior" ⓘ
Brillouin function reduces to Langevin function for J → ∞ via predicate surface "limitCase" NERFINISHED ⓘ
Brillouin function linear in x for small x via predicate surface "limitCase" ⓘ
Brillouin function saturates to 1 for large positive x via predicate surface "limitCase" ⓘ
Brillouin function saturates to -1 for large negative x via predicate surface "limitCase" ⓘ
Burkert profile ρ(r) ∝ r⁻³ at large radii via predicate surface "asymptoticBehavior" ⓘ
Gram points g_n grows roughly like 2πn / log(n) for large n (up to lower-order terms) via predicate surface "asymptoticBehavior" ⓘ
Langevin function L(x) → 1 as x → ∞ ⓘ
Langevin function L(x) → −1 as x → −∞ ⓘ
Langevin function L(x) ≈ x/3 for small x ⓘ
q-Selberg integral Selberg integral via predicate surface "limitAs q→1" NERFINISHED ⓘ
Chinese restaurant process number of occupied tables grows like O(α log n) ⓘ
Koebe function k(r) \to +\infty as r \to 1^- along positive real axis via predicate surface "hasAsymptoticBehavior" ⓘ
Koebe function k(-r) \to -1/4 as r \to 1^- along negative real axis via predicate surface "hasAsymptoticBehavior" ⓘ
Fisher zeros condense into curves or areas in the thermodynamic limit ⓘ