Equivalence relation | Wikipedia audio article
Channel: wikipedia tts
Date: 04/10/2019

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Equivalence_relation


00:00:22 1 Notation
00:00:35 2 Definition
00:00:45 3 Examples
00:01:08 3.1 Simple example
00:01:55 3.2 Equivalence relations
00:03:05 3.3 Relations that are not equivalences
00:03:13 4 Connections to other relations
00:04:46 5 Well-definedness under an equivalence relation
00:05:58 6 Equivalence class, quotient set, partition
00:07:33 6.1 Equivalence class
00:10:17 6.2 Quotient set
00:11:43 6.3 Projection
00:12:08 6.4 Equivalence kernel
00:12:56 6.5 Partition
00:13:39 6.5.1 Counting possible partitions
00:14:24 7 Fundamental theorem of equivalence relations
00:14:45 8 Comparing equivalence relations
00:14:50 9 Generating equivalence relations
00:15:29 10 Algebraic structure
00:15:56 10.1 Group theory
00:16:59 10.2 Categories and groupoids
00:17:55 10.3 Lattices
00:19:15 11 Equivalence relations and mathematical logic
00:21:46 12 Euclidean relations
00:23:15 13 See also
00:23:56 14 Notes
00:26:32 15 References
00:27:54 16 External links
00:28:35 Equivalence relations and mathematical logic
00:30:26 Euclidean relations
00:31:35 (aRa ∧ bRa) → aRb [reflexive; erase T∧]
00:32:24 See also



Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago.

Learning by listening is a great way to:
- increases imagination and understanding
- improves your listening skills
- improves your own spoken accent
- learn while on the move
- reduce eye strain

Now learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while you are sleeping! If you are planning to listen a lot, you could try using a bone conduction headphone, or a standard speaker instead of an earphone.

Listen on Google Assistant through Extra Audio:
https://assistant.google.com/services/invoke/uid/0000001a130b3f91
Other Wikipedia audio articles at:
https://www.youtube.com/results?search_query=wikipedia+tts
Upload your own Wikipedia articles through:
https://github.com/nodef/wikipedia-tts
Speaking Rate: 0.8872885385787985
Voice name: en-AU-Wavenet-A


"I cannot teach anybody anything, I can only make them think."
- Socrates


SUMMARY
=======
In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive. The relation "is equal to" is the canonical example of an equivalence relation, where for any objects a, b, and c:

a = a (reflexive property),
if a = b then b = a (symmetric property), and
if a = b and b = c then a = c (transitive property).As a consequence of the reflexive, symmetric, and transitive properties, any equivalence relation provides a partition of the underlying set into disjoint equivalence classes. Two elements of the given set are equivalent to each other if and only if they belong to the same equivalence class.