Ad
related to: inductive reasoning geometry
Search results
Results From The WOW.Com Content Network
Despite its name, mathematical induction differs fundamentally from inductive reasoning as used in philosophy, in which the examination of many cases results in a probable conclusion. The mathematical method examines infinitely many cases to prove a general statement, but it does so by a finite chain of deductive reasoning involving the ...
Inductive reasoning is any of various methods of reasoning in which broad generalizations or principles are derived from a body of observations. [1] [2] This article is concerned with the inductive reasoning other than deductive reasoning (such as mathematical induction), where the conclusion of a deductive argument is certain given the premises are correct; in contrast, the truth of the ...
Despite its name, mathematical induction is a method of deduction, not a form of inductive reasoning. In proof by mathematical induction, a single "base case" is proved, and an "induction rule" is proved that establishes that any arbitrary case implies the next case.
While deductive logic allows one to arrive at a conclusion with certainty, inductive logic can only provide a conclusion that is probably true. [non-primary source needed] It is mistaken to frame the difference between deductive and inductive logic as one between general to specific reasoning and specific to general reasoning. This is a common ...
Bacon's method is an example of the application of inductive reasoning. However, Bacon's method of induction is much more complex than the essential inductive process of making generalisations from observations.
The triangle is one of the basic shapes in geometry. Logic – formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science.
William Whewell found the "inductive sciences" not so simple, but, amid the climate of esteem for inductivism, described "superinduction". [86] Whewell proposed recognition of "the peculiar import of the term Induction", as "there is some Conception superinduced upon the facts", that is, "the Invention of a new Conception in every inductive ...
This led to a natural curiosity with regards to geometry and trigonometry – particularly triangles and rectangles. These were the shapes which provided the most questions in terms of practical things, so early geometrical concepts were focused on these shapes, for example, the likes of buildings and pyramids used these shapes in abundance.