Rigorous proof in mathematics is often derived from deductive and inductive reasoning. Deductive reasoning is the premise to achieve complete certainty: it is defined as "reasoning from general to particular" (Lagemaat 121). ... Mathematicians use inductive reasoning to expand on axioms to form truths. ... It expresses how evidence comes to bear on hypotheses (Inductive Logic). ... However, Fermat had to surpass inductive and deductive reasoning by using imagination to create a completely new equation x³+y³=z³ based on his previous knowledge of Pythagorean theory and attempt to s...

• Word Count: 1304
• Approx Pages: 5
• Has Bibliography
• Grade Level: Undergraduate

This method of study is called inductive reasoning: observing as many examples as possible and then, based on these observations, working out a basic principle they have in common. Inductive reasoning is the basis of the western scientific method. ... Two kinds of logic were used by Aristotle: deductive, which led to certain conclusions and inductive which led to probable conclusions. He is famous for the syllogism (deductive reasoning) that takes two truths, connects them, and comes up with a third statement that is also true. ... He also used inductive reasoning to go from specific statem...

• Word Count: 2430
• Approx Pages: 10
• Has Bibliography
• Grade Level: High School

Also everything which is provided by scientists is based on inductive reasoning which is unacceptable. Inductive reasoning is sort of reasoning which is looking for some evidences based on small-scale and repetitive observations to get (not exact proof of) the truth. While the deductive reasoning is exact, certain and absolutely acceptable. Based on evidence given inductive argument's conclusions might be probable. All in all, in science no one can accept inductive reasoning without sufficient evidences; Second of all, if we accept that there will be a danger for human life and we know it...

• Word Count: 1433
• Approx Pages: 6
• Has Bibliography