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A conflation is a mistake in which two or more separate but similar ideas become confused with one another.


The trivial quotient on a set is the mapping $q_{\Delta_S}: S \to S / \Delta_S: $ defined as:

$\forall x \in S: q_{\Delta_S} \left({x}\right) = \left\{{x}\right\}$

where $\Delta_S$ is the diagonal relation on $S$.

This can become conflated with the identity mapping $I_S: S \to S$ defined as:

$\forall x \in S: I_S \left({x}\right) = x$

The image of an element under the identity mapping is that element.

The image of an element under the trivial quotient is a singleton set containing just that element.

The two are completely different.