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Another variant, called complete induction, course of values induction or strong induction (in contrast to which the basic form of induction is sometimes known as weak induction), makes the induction step easier to prove by using a stronger hypothesis: one proves the statement (+) under the assumption that () holds for all natural numbers less ...
Inductive reasoning is any of various methods of reasoning in which broad generalizations or principles are derived from a body of observations. [1] [2] Inductive reasoning is in contrast to 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 conclusion of an inductive ...
Unlike many other forms of syllogism, a statistical syllogism is inductive, so when evaluating this kind of argument it is important to consider how strong or weak it is, along with the other rules of induction (as opposed to deduction). In the above example, if 99% of people are taller than 26 inches, then the probability of the conclusion ...
See inductive argument, induction on well-formed formulas, mathematical induction, strong mathematical induction, transfinite induction, weak mathematical induction induction on well-formed formulas A method used in formal logic and mathematics to prove properties of all well-formed formulas by showing they hold for basic formulas and are ...
Strong and weak sampling are two sampling approach [1] in Statistics, and are popular in computational cognitive science and language learning. [2] In strong sampling, it is assumed that the data are intentionally generated as positive examples of a concept, [3] while in weak sampling, it is assumed that the data are generated without any restrictions.
Argument from analogy is a special type of inductive argument, where perceived similarities are used as a basis to infer some further similarity that has not been observed yet. Analogical reasoning is one of the most common methods by which human beings try to understand the world and make decisions. [ 1 ]
Furthermore, I think the entire section of strong vs. weak induction is pretty, well -- weak. Once you realize that additional cases don't have any bearing on the truth or falsity of a proposition, you'll see that they are, in reality, no different (unless you're one of the very few that foolishly defends probabilistic induction). -Tris
In general topology and related areas of mathematics, the final topology [1] (or coinduced, [2] weak, colimit, or inductive [3] topology) on a set, with respect to a family of functions from topological spaces into , is the finest topology on that makes all those functions continuous.