Neither wikipedia nor the first few pages of Google are showing me much about the history of the development of equivalence classes. When was this notion first formalized?
2026-04-12 10:49:40.1775990980
When were equivalence classes formalized?
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As recommended by Alan, I asked this question over on hsm.SE.
Conifold captured some of the historical messiness in their answer. I recommend you read his answer, but the gist is that the notion was being developed near the start of the 20th century. Reference together of the modern name and formal definition of equivalence classes existed as early as the 1930's.