... examining their reliance on reasoning and imagination. 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). When applied to a system of numbers, real numbers can be narrowed down to different factors: irrational, rational, and whole numbers ... a completely new equation x³+y³=z³ based on his previous knowledge of Pythagorean theory and attempt to solve it (11.01.00). To elaborate, Euclid imagined a perfect pentagon...

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