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The quantity—a cardinal number—is associated with the set, and is invariant under the process of counting.
In “Toward a Theory of Race, Crime, and Urban Inequality,” Sampson and Wilson (1995) argued that racial disparities in violent crime are attributable in large part to the persistent structural disadvantages that are disproportionately concentrated in African American communities.
They also argued that the ultimate causes of crime were similar for both Whites and Blacks, leading to what has been labeled the thesis of “racial invariance.” In light of the large scale social changes of the past two decades and the renewed political salience of race and crime in the United States, this paper reassesses and updates evidence evaluating the theory.
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More generally, an invariant with respect to an equivalence relation is a property that is constant on each equivalence class.
Invariants are used in diverse areas of mathematics such as geometry, topology, algebra and discrete mathematics.
There are also inequalities that remain true when the values of their variables change.
The distance between two points on a number line is not changed by adding the same quantity to both numbers.
These transformations produce similar shapes, which is the basis of trigonometry.
In contrast, angles and ratios are not invariant under non-uniform scaling (such as stretching).