What does extension mean in math?

In mathematics, the ‘extension’ of a mathematical concept is the set that is specified by. . (That set might be empty, currently.) For example, the extension of a function is a set of ordered pairs that pair up the arguments and values of the function; in other words, the function’s graph.

What does generalize mean to mathematicians?

generalization
In mathematics, generalization can be both a process and a product. When one looks at specific instances, notices a pattern, and uses inductive reasoning to conjecture a statement about all such patterns, one is generalizing.

What does it mean to generalize a formula?

A generalization is a form of abstraction whereby common properties of specific instances are formulated as general concepts or claims. Generalizations posit the existence of a domain or set of elements, as well as one or more common characteristics shared by those elements (thus creating a conceptual model).

What are the types of generalization?

These clarified terms allow us to identify four distinct forms of generalizing (everyday inductive generalizing, everyday deductive generalizing, academic inductive generalizing, and academic deductive generaliz- ing), each of which we illustrate with an information systems-related example.

What is the extension of a term?

extension, in logic, correlative words that indicate the reference of a term or concept: “intension” indicates the internal content of a term or concept that constitutes its formal definition; and “extension” indicates its range of applicability by naming the particular objects that it denotes.

What is principle of extension in discrete mathematics?

The statement that every partial order can be extended to a total order is known as the order-extension principle. Applying the order-extension principle to a partial order in which every two elements are incomparable shows that (under this principle) every set can be linearly ordered.

What is Generalisation discuss the role of Generalisation in history?

A generalisation is a linkage of disparate or unrelated facts, in time or space, with each other. It is their grouping, their rational classification. More widely, generalisations are the means through which historians understand their materials and try to provide their understanding of facts to others.

What is the difference between generalization and abstraction?

While abstraction reduces complexity by hiding irrelevant detail, generalization reduces complexity by replacing multiple entities which perform similar functions with a single construct.

Why do we generalize?

We make generalizations about objects in order to make sense of the world. When we see something, we want to know what it is and how to react to and interact with it. We generalize about more than just objects; we generalize about people so that we know how to interact with them.

What does it mean to generalize results?

Generalizability is applied by researchers in an academic setting. It can be defined as the extension of research findings and conclusions from a study conducted on a sample population to the population at large. The larger the sample population, the more one can generalize the results.

How do comprehension and extension relate each other?

These two properties of the idea are in inverse ratio to each other: the greater the comprehension of an idea, the less its extension, and vice versa.

What is narrowing in linguistics?

Semantic narrowing is a type of semantic change by which the meaning of a word becomes less general or inclusive than its earlier meaning. The opposite process is called broadening or semantic generalization. “Such specialization is slow and need not be complete,” notes linguist Tom McArthur.