# Definition:Conflation

## Definition

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:

$\forall x \in S: \map {q_{\Delta_S} } x = \set x$

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

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

$\forall x \in S: \map {I_S} x = x$

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.