Definition:Conflation

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

Example
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.