The notion of inequality refers to the lack of equality. Two things, therefore, are unequal when they are not equal: that is, when they are dissimilar, asymmetrical or different.

The concept is used in multiple fields. In the field of mathematics, inequality refers to the order relationship that is established between values that are different. This means that one value can be greater or less than another, but not identical; if both were equal, then we would speak of *equality*. See Abbreviation Finder for acronyms related to Inequality.

The concept of *order relation*, for its part, is also known as *order in R*, and it is a binary relation that pursues the order of the sets through the distribution of its elements. When the values of an inequality are elements that belong to an ordered set, such as real numbers or integers, it is possible to compare them with each other. In this way, the doors are opened to notations such as the following:

* a < b, which is defined as a relation in which the first element is less than the second;

* a > b, which tells us that the first element is greater than the second.

These two examples belong to the group of strict inequalities, all those in which the first element cannot be equal to the second; in both cases, we can read the notations as “strictly less/greater than”. On the other hand we have the wide (also known as *non-strict) *inequalities, which are used very frequently in the field of computer programming; they are represented with the following two notations: a ≤ b and a ≥ b, which are used to say that the first element is “less than or equal to” or “greater than or equal to” the second, respectively.

The possibilities that inequality gives us to compare elements do not end here, since we also have the sign ≪ and its opposite, ≫, which allow us to speak of elements “much smaller than” or “much larger than” others, respectively. This type of relationship usually indicates a considerable difference, in which there are *several orders of magnitude*, that is, “several zeros” between one number and another.

If we simply want to say that one element *is not equal to another*, we can resort to the ≠ sign, to give rise to a notation like a ≠ b. In this case, it is not clear if one is greater than the other, since we also do not know if it is possible to compare them.

The idea of social inequality, for its part, is linked to what happens when people live in conditions or situations that are dissimilar. In these cases there is discrimination, which can be negative or positive according to the detriment or benefit of the individual in question.

We can speak of income inequality when the distribution of income from work and capital is not distributed equally. If workers living in the north of a given country have an average salary of 5,000 currency units, while those living in the south earn an average of 3,800 currency units, an income inequality is recorded in favor of those who live in the northern region.

Social inequality is a broader idea that usually encompasses different factors: access to education, health services, well-paid jobs, etc. There are people who, because of their place of birth, find it very difficult to progress materially since they did not go to school, had to work from an early age and live in precarious homes. Others, on the other hand, have advantages due to their family origins (quality education, comforts to study and live, contacts in the world of work, etc.). There is, therefore, a marked social inequality that conditions existence.