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By the definition of a rational number, the statement can be made that "If is rational, then it can be expressed as an irreducible fraction". This statement is true because it is a restatement of a definition.
More broadly, proof by contradiction is any form of argument that establishes a statement by arriving at a contradiction, even when the initial assumption is not the negation of the statement to be proved. In this general sense, proof by contradiction is also known as indirect proof, proof by assuming the opposite, [2] and reductio ad ...
Complementary antonyms are word pairs whose meanings are opposite but whose meanings do not lie on a continuous spectrum (push, pull). Relational antonyms are word pairs where opposite makes sense only in the context of the relationship between the two meanings (teacher, pupil). These more restricted meanings may not apply in all scholarly ...
Popper proposed falsifiability as the cornerstone solution to both the problem of induction and the problem of demarcation. He insisted that, as a logical criterion, his falsifiability is distinct from the related concept "capacity to be proven wrong" discussed in Lakatos's falsificationism.
Positivism is a philosophical school that holds that all genuine knowledge is either true by definition or positive – meaning a posteriori facts derived by reason and logic from sensory experience. [ 1 ] [ 2 ] Other ways of knowing , such as intuition , introspection , or religious faith , are rejected or considered meaningless .
Metaphysics is the study of the most general features of reality, including existence, objects and their properties, possibility and necessity, space and time, change, causation, and the relation between matter and mind.
Anaximander posited that every element had an opposite, or was connected to an opposite (water is cold, fire is hot). Thus, the material world was said to be composed of an infinite, boundless apeiron from which arose the elements (earth, air, fire, water) and pairs of opposites (hot/cold, wet/dry).
An omnibus bill is a proposed law that covers a number of diverse or unrelated topics. Omnibus is derived from Latin and means "to, for, by, with or from everything". An omnibus bill is a single document that is accepted in a single vote by a legislature but packages together several measures into one or combines diverse subjects.