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In a conclusion, when we use deduction we reason from general principles to specific cases, as in applying a mathematical theorem to a particular problem or in citing a law of physics to predict the outcome of an experiment.
In a validdeductive argument, all of the content of the conclusion is present, at least implicitly, in the premises.
Induction Step: For k ≥ 1 assume that the claim is true for h = k and prove that it is true for h = k+1.
Induction is the conscious mental process by which we pass from the perception of particular phenomena (things and events) to the knowledge of general truths.
Although induction is equally applicable in all departments of generalization from experience, in the historical and anthropological no less than in the physical sciences, still it is in its application to the discovery of the causes and laws of physical phenomena, animate and inanimate, that it lends itself most readily to logical analysis.
Induction is really a logical method involving many stages and processes besides the central step of generalization itself; and it is opposed to deduction only in the sense that it approaches reality from the side of the concrete and individual, while deduction does so from that of the abstract and universal.
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