givesBoundOn
P96513
predicate
Indicates that one quantity provides an upper or lower limit (a bound) on the value or behavior of another quantity.
Observed surface forms (14)
- errorBound ×3
- givesUpperBoundOn ×3
- givesBound ×2
- givesLowerBoundInTermsOf ×2
- givesLowerBoundOn ×2
- givesUpperBoundFor ×2
- hasUpperBound ×2
- isLowerBoundOn ×2
- boundednessProperty ×1
- collisionProbabilityBound ×1
- impliesUnderBoundedOnInterval ×1
- originalBound ×1
- upperBoundExpression ×1
- upperBoundGivenBy ×1
Sample triples (31)
| Subject | Object |
|---|---|
| Koebe quarter theorem | size of image of univalent function ⓘ |
| Koebe quarter theorem | inner radius of image domain ⓘ |
| Hurwitz bound on automorphism groups of curves | order of the automorphism group of a compact Riemann surface via predicate surface "givesUpperBoundFor" ⓘ |
| Hurwitz bound on automorphism groups of curves | order of the automorphism group of a smooth projective algebraic curve of genus g ≥ 2 over C via predicate surface "givesUpperBoundFor" ⓘ |
| Hurwitz bound on automorphism groups of curves | 84(g − 1) via predicate surface "upperBoundExpression" ⓘ |
| Milnor–Wood inequality | Euler class of flat circle bundles ⓘ |
| Milnor–Wood inequality | Euler number of representations into Homeo^+(S^1) ⓘ |
| Bernstein inequalities | tail probabilities of sums of random variables via predicate surface "givesUpperBoundOn" ⓘ |
| Bernstein inequalities | supremum norm of derivatives of polynomials via predicate surface "givesUpperBoundOn" ⓘ |
| Happy Ending problem | f(n) ≤ {2n-4 \choose n-2} + 1 (classical Erdős–Szekeres bound) via predicate surface "hasUpperBound" ⓘ |
| Erdős–Szekeres theorem | ES(n) ≤ \binom{2n-4}{n-2} + 1 via predicate surface "originalBound" ⓘ |
| Cauchy functional equation | f(x) = ax for some constant a via predicate surface "impliesUnderBoundedOnInterval" ⓘ |
| Banach limit | |L(x)|≤sup_n|x_n| for all bounded sequences x via predicate surface "boundednessProperty" ⓘ |
| Krull’s principal ideal theorem | height of prime ideals minimal over a principal ideal via predicate surface "givesBound" ⓘ |
| Alon–Boppana bound | spectral gap between d and the second-largest eigenvalue via predicate surface "isLowerBoundOn" ⓘ |
| source coding theorem | H(X)+1 for optimal prefix codes of a discrete memoryless source via predicate surface "upperBoundGivenBy" ⓘ |
| Fano inequality | probability of misclassification via predicate surface "givesLowerBoundOn" ⓘ |
| Fano inequality | probability of decoding error via predicate surface "givesLowerBoundOn" ⓘ |
| Dedekind number | 2^(binomial(n,⌊n/2⌋)(1+o(1))) via predicate surface "hasUpperBound" ⓘ |
| Dirichlet approximation theorem | approximation error less than 1/(qN) via predicate surface "errorBound" ⓘ |
| Dirichlet approximation theorem | approximation error less than 1/q² for infinitely many rationals via predicate surface "errorBound" ⓘ |
|
Roth theorem
surface form:
Roth's theorem
|
irrationality measure of algebraic numbers ⓘ |
| Arnold conjecture | sum of Betti numbers of the manifold via predicate surface "givesLowerBoundInTermsOf" ⓘ |
| Arnold conjecture | Lusternik–Schnirelmann category in some variants via predicate surface "givesLowerBoundInTermsOf" ⓘ |
| GHASH | proportional to number of blocks squared divided by 2^128 via predicate surface "collisionProbabilityBound" ⓘ |
|
complexity class BPP
surface form:
BPP
|
bounded away from 1/2 via predicate surface "errorBound" ⓘ |
| Koksma–Hlawka inequality | absolute integration error via predicate surface "givesUpperBoundOn" ⓘ |
| ELBO | log p(x) via predicate surface "isLowerBoundOn" ⓘ |
| Siegel–Walfisz theorem | error term that is smaller than any fixed power of log x via predicate surface "givesBound" ⓘ |
| Burger–Iozzi–Wienhard inequalities for higher rank groups | Toledo invariant of a representation NERFINISHED ⓘ |
| Burger–Iozzi–Wienhard inequalities for higher rank groups | norm of pullback of bounded Kähler class ⓘ |