a relation that is reflexive, symmetric, and transitive: it imposes a partition on its domain of definition so that two elements belong to the same subset if and only if the relation holds between them
equivalence relation in American English
noun
Math
a relation that is reflexive, symmetrical, and transitive, as equality
Word origin
[1945–50]This word is first recorded in the period 1945–50. Other words that entered Englishat around the same time include: RNA, ergative, poison pill, shootout, spin-off
Examples of 'equivalence relation' in a sentence
equivalence relation
Next, using the kernels of homomorphisms, we define an equivalence relation on this topological space.
Fatma Özdemir, Hasan Özekes 2013, 'On the Homomorphisms of the Lie Groups and', Abstract and Applied Analysishttp://dx.doi.org/10.1155/2013/645848. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
We also prove an equivalence relation between vortex defects and 0d-2d coupled systems.
Kazuo Hosomichi, Sungjay Lee, Takuya Okuda 2018, 'Supersymmetric vortex defects in two dimensions', Journal of High Energy Physicshttp://link.springer.com/article/10.1007/JHEP01(2018)033. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
It involves the equivalence relation generated by reset maps of a hybrid system.
Leth John, Wisniewski Rafael 2014, 'Local analysis of hybrid systems on polyhedral sets with state-dependent switching',International Journal of Applied Mathematics and Computer Sciencehttp://www.degruyter.com/view/j/amcs.2014.24.issue-2/amcs-2014-0026/amcs-2014-0026.xml?format=INT. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Then, the relationships among information entropy sequence, hierarchical quotient space structure, fuzzy equivalence relation, and fuzzy similarity relation are analyzed.
Qinghua Zhang, Guoyin Wang 2011, 'The Uncertainty Measure of Hierarchical Quotient Space Structure', Mathematical Problems in Engineeringhttp://dx.doi.org/10.1155/2011/513195. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
In particular, we construct an ordered regular equivalence relation on an ordered semihypergroup by a weak pseudoorder.
Tang Jian, Feng Xinyang, Davvaz Bijan, Xie Xiang-Yun 2018, 'A further study on ordered regular equivalence relations in ordered semihypergroups',Open Mathematicshttp://www.degruyter.com/view/j/math.2018.16.issue-1/math-2018-0016/math-2018-0016.xml?format=INT. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
We define an equivalence relation on propositions and a proof system where equivalent propositions have the same proofs.
Alejandro Díaz-Caro, Gilles Dowek 2013, 'Non determinism through type isomorphism', Electronic Proceedings in Theoretical Computer Sciencehttp://arxiv.org/pdf/1303.7334v1. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
This fact will be realised by using an equivalence relation among the web pages of the web application.
Doru Anastasiu Popescu, Maria Catrinel Dănăuţă 2012, 'Validation of a Web Application by Using a Limited Number of Web Pages', Brain: Broad Research in Artificial Intelligence and Neurosciencehttp://brain.edusoft.ro/index.php/brain/article/view/304. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Further, we define the q-rung picture fuzzy equivalence relation and q-rung picture fuzzy hierarchical quotient space structures.
Anam Luqman, Muhammad Akram, Ali N. A. Koam 2019, 'Granulation of Hypernetwork Models under the q-Rung Picture Fuzzy Environment', Mathematicshttps://www.mdpi.com/2227-7390/7/6/496. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)