monotoneIn
P10675
predicate
Indicates that the relationship or function preserves a specified order when one of its arguments increases, meaning larger inputs (in that argument) do not lead to smaller outputs with respect to the given ordering.
All labels observed (14)
| Label | Occurrences |
|---|---|
| monotonicity | 4 |
| monotoneIn canonical | 2 |
| isMonotone | 1 |
| isMonotoneInIndex | 1 |
| isMonotoneUnder | 1 |
| isMonotoneWithRespectTo | 1 |
| isMonotonic | 1 |
| isMonotonicFunctionOf | 1 |
| monotoneUnder | 1 |
| monotoneWithRespectTo | 1 |
| monotonic | 1 |
| monotonicWith | 1 |
| monotonicWithinWrap | 1 |
| monotonicityProperty | 1 |
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: monotoneIn
Generated description
Indicates that the relationship or function preserves a specified order when one of its arguments increases, meaning larger inputs (in that argument) do not lead to smaller outputs with respect to the given ordering.
Sample triples (18)
| Subject | Object |
|---|---|
| Rényi entropy | order parameter α for fixed distribution ⓘ |
| Minkowski sum | true via predicate surface "isMonotone" ⓘ |
| Rényi divergence | order α ⓘ |
|
Boltzmann–Gibbs entropy in statistical mechanics
surface form:
Boltzmann–Gibbs entropy
|
number of accessible microstates via predicate surface "monotonicWith" ⓘ |
| Carathéodory metric | domain inclusion via predicate surface "isMonotoneWithRespectTo" ⓘ |
| ReLU | true via predicate surface "monotonic" ⓘ |
| Fitting ideal | yes via predicate surface "isMonotoneInIndex" ⓘ |
|
Chebyshev functions
surface form:
Chebyshev function θ(x)
|
non-decreasing in x via predicate surface "monotonicity" ⓘ |
| golden ratio | square root of 5 via predicate surface "isMonotonicFunctionOf" ⓘ |
| Hermite constant | nondecreasing in n via predicate surface "monotonicity" ⓘ |
| Kobayashi metric | holomorphic mappings via predicate surface "isMonotoneUnder" ⓘ |
| Catalan numbers | C_n is strictly increasing for n ≥ 1 via predicate surface "monotonicity" ⓘ |
| von Neumann entropy | completely positive trace-preserving maps for appropriate combinations via predicate surface "monotoneUnder" ⓘ |
| Hausdorff dimension | set inclusion via predicate surface "monotoneWithRespectTo" ⓘ |
| Farey sequence | F_n is a subsequence of F_{n+1} via predicate surface "monotonicity" ⓘ |
| Dowdall system | monotone under standard interpretations via predicate surface "monotonicityProperty" ⓘ |
| Brillouin function | true via predicate surface "isMonotonic" ⓘ |
| GetTickCount | non-decreasing until wraparound occurs via predicate surface "monotonicWithinWrap" ⓘ |