Logical reasoning & Mathematical proof - Unionpedia, the concept map

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Difference between Logical reasoning and Mathematical proof

Logical reasoning vs. Mathematical proof

Logical reasoning is a mental activity that aims to arrive at a conclusion in a rigorous way. A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion.

Argument

An argument is a series of sentences, statements, or propositions some of which are called premises and one is the conclusion.

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Deductive reasoning

Deductive reasoning is the process of drawing valid inferences.

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Empirical evidence

Empirical evidence for a proposition is evidence, i.e. what supports or counters this proposition, that is constituted by or accessible to sense experience or experimental procedure.

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Formal language

In logic, mathematics, computer science, and linguistics, a formal language consists of words whose letters are taken from an alphabet and are well-formed according to a specific set of rules called a formal grammar.

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Inductive reasoning

Inductive reasoning is any of various methods of reasoning in which broad generalizations or principles are derived from a body of observations.

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Inference

Inferences are steps in reasoning, moving from premises to logical consequences; etymologically, the word infer means to "carry forward".

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Informal logic

Informal logic encompasses the principles of logic and logical thought outside of a formal setting (characterized by the usage of particular statements).

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Logic

Logic is the study of correct reasoning.

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Natural language

In neuropsychology, linguistics, and philosophy of language, a natural language or ordinary language is any language that occurs naturally in a human community by a process of use, repetition, and change without conscious planning or premeditation.

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Natural number

In mathematics, the natural numbers are the numbers 0, 1, 2, 3, etc., possibly excluding 0.

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Probability

Probability is the branch of mathematics concerning events and numerical descriptions of how likely they are to occur.

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Proposition

A proposition is a central concept in the philosophy of language, semantics, logic, and related fields, often characterized as the primary bearer of truth or falsity.

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Rule of inference

In philosophy of logic and logic, a rule of inference, inference rule or transformation rule is a logical form consisting of a function which takes premises, analyzes their syntax, and returns a conclusion (or conclusions).

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