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Random information on the term “Attainment”:
In sociology, status attainment or status attainment theory deals largely with one’s position in society, or class. Status attainment is affected by both achieved factors, such as educational attainment, and ascribed factors, such as family income. It is achieved by a combination of parents’ status and one’s own efforts and abilities. The idea behind status attainment is that one can be mobile, either upwardly or downwardly, in the form of a class system.
Peter M. Blau (1918–2002) and Otis Duncan (1921–2004) were the first sociologists to isolate the concept of status attainment. Their initial thesis stated that the lower the level from which a person starts, the greater is the probability that he will be upwardly mobile, simply because many more occupational destinations entail upward mobility for men with low origins than for those with high ones. After continued research, the initial statement proved to be incorrect. Blau and Duncan realized that people couldn’t possibly think that the best way to get a high-social status position is to start at the bottom. They continued to find that the flaw was in the question the information was based upon. They found their research shouldn’t be founded upon the question of “How are people mobile” but on “how do people attain their statuses”. Peter Blau and Otis Duncan continued to conduct a landmark research study to provide answers to their new question..
Random information on the term “undefined”:
In mathematics, the term undefined is often used to refer to an expression which is not assigned an interpretation or a value (such as an indeterminate form, which has the propensity of assuming different values). The term can take on several different meanings depending on the context. For example:
In ancient times, geometers attempted to define every term. For example, Euclid defined a point as “that which has no part”. In modern times, mathematicians recognize that attempting to define every word inevitably leads to circular definitions, and therefore leave some terms (such as “point”) undefined (see primitive notion for more).
This more abstract approach allows for fruitful generalizations. In topology, a topological space may be defined as a set of points endowed with certain properties, but in the general setting, the nature of these “points” is left entirely undefined. Likewise, in category theory, a category consists of “objects” and “arrows”, which are again primitive, undefined terms. This allows such abstract mathematical theories to be applied to very diverse concrete situations.