THEOREM Meaning and
Definition
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A theorem is a fundamental concept in mathematics and logic that plays a crucial role in proving mathematical statements or propositions. It refers to a statement that has been proven or demonstrated to be true, based on a series of logical deductions from previously established truths or axioms. Theorems are of immense importance in mathematics as they provide logical reasoning and evidence for asserting the validity of mathematical claims.
A theorem consists of two main components: the hypotheses and the conclusions. The hypotheses are the assumptions or conditions upon which the theorem is based, while the conclusions are the mathematical statements that can be deduced or derived from those hypotheses. A theorem often follows a specific format, beginning with an "if-then" statement that connects the hypotheses to the conclusions.
The process of proving a theorem involves a logical sequence of steps, starting from the assumptions or previously proven theorems and employing the principles of deductive reasoning. This process aims to demonstrate that the conclusions of the theorem are true under the given assumptions or conditions. Once a theorem is proven, it is considered valid and can serve as a foundation for solving additional mathematical problems or building upon further theorems.
Theorems are not limited to mathematics and logic, as they can also exist in other scientific disciplines. In these fields, theorems provide a similar framework of logical reasoning and evidential support for proving scientific theories or hypotheses. Overall, the concept of a theorem represents a significant and indispensable tool in the pursuit of knowledge and understanding in various disciplines.
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In math., something laid down as a truth which is to be proved by a chain of reasoning; in analysis, a rule or statement of relations expressed in a formula or by symbols.
Etymological and pronouncing dictionary of the English language. By Stormonth, James, Phelp, P. H. Published 1874.
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Other Common Misspellings for THEOREM
Etymology of THEOREM
The word "theorem" originated from the Greek word "theōrein", which means "to look at" or "to observe". "Theōrein" is derived from the combination of "thea" (meaning "eye" or "sight") and "horan" (meaning "to see" or "to observe"). Therefore, etymologically, "theorem" refers to something that is "to be looked at" or "to be observed".
Similar spelling words for THEOREM
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