What is the difference between theorems and theories

A doctrine, or scheme of things, which terminates in speculation or contemplation, without a view to practice; hypothesis; speculation. An exposition of the general or abstract principles of any science; as, the theory of music. The science, as distinguished from the art; as, the theory and practice of medicine. In mathematics and logic, a theorem is a non-self-evident statement that has been proven to be true, either on the basis of generally accepted statements such as axioms or on the basis of previously established statements such as other theorems.

A theorem is hence a logical consequence of the axioms, with a proof of the theorem being a logical argument which establishes its truth through the inference rules of a deductive system. The philosophical explanation of phenomena, either physical or moral; as, Lavoisier's theory of combustion; Adam Smith's theory of moral sentiments. A theory is a rational type of abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking is often associated with such processes as observational study or research.

Published: 28 Dec, Theorem noun mathematics A mathematical statement of some importance that has been proven to be true. Theory noun obsolete Mental conception; reflection, consideration. Theory noun sciences A coherent statement or set of ideas that explains observed facts or phenomena and correctly predicts new facts or phenomena not previously observed, or which sets out the laws and principles of something known or observed; a hypothesis confirmed by observation, experiment etc.

Theorem noun logic A syntactically correct expression that is deducible from the given axioms of a deductive system. Theory noun uncountable The underlying principles or methods of a given technical skill, art etc.

Theorem verb transitive To formulate into a theorem. Theory noun mathematics A field of study attempting to exhaustively describe a particular class of constructs. Theorem noun That which is considered and established as a principle; hence, sometimes, a rule. Theory noun A hypothesis or conjecture. Theorem noun A statement of a principle to be demonstrated. Theory noun A set of axioms together with all statements derivable from them.

Theorem verb To formulate into a theorem. Theory noun A doctrine, or scheme of things, which terminates in speculation or contemplation, without a view to practice; hypothesis; speculation. Theorem noun a proposition deducible from basic postulates. Theory noun An exposition of the general or abstract principles of any science; as, the theory of music.

Theorem noun an idea accepted as a demonstrable truth. Theory noun The science, as distinguished from the art; as, the theory and practice of medicine. Theorem In mathematics and logic, a theorem is a non-self-evident statement that has been proven to be true, either on the basis of generally accepted statements such as axioms or on the basis of previously established statements such as other theorems. Theory noun The philosophical explanation of phenomena, either physical or moral; as, Lavoisier's theory of combustion; Adam Smith's theory of moral sentiments.

Theory A theory is a rational type of abstract thinking about a phenomenon, or the results of such thinking. As you can see, if you start off with a poor or misguided understanding in mathematics, it just may take you down a path to paradoxical theories, like Quantum Theory and Relativity.

Paradoxes are a sign that it is not your theory that is flawed, but the axioms that the theory is supported upon is in error. Just imagine, two hundred years of the greatest mathematical minds and greatest physicists in history all missed one important and minor thing, like understanding what the dot product really is. Could this really be true? Its not like its ever happened before is it? Hmmm, two and half thousand years of believing that the Earth was the center of the known universe, does come to mind.

I gave you an argument earlier that linear thinking is dangerous. For it brainwashes people into thinking one way. I can tell you now, there are very deep problems and mistakes we have made in physics and mathematics, all because, we do mathematical physics and not physical mathematics.

How many centuries must past before humanity learns these lessons? It is rigorous, and looks prety good. Thanks for this nice post and the follow-up discussions, I was looking for quite sometime.

Why not include the dictionary meanings giving references of these terms to give more authenticity to the definitions!

This site is really helpful to all the students of Mathematics and the definitions you provided are somehow true but not absolutely true or true all the time. I know you considered your audience but I believe we have to consider the truth first before anything else. You may go with the definitions that you have but you must not forget to remind your students that the world of Mathematics is not linear and can be anything they think as long as they can prove it just like what other Mathematics lovers are saying, relax…prove a theorem.

Other potentially interesting ways to explore the relationships between these statements would be [1] Venn diagrams and [2] concept maps. The point is that using non-traditional means to explore learning can be very cool and illuminating. Usually, I start by saying that a Theorem is something that may or may not seem likely, but can be proven by logical building blocks, postulates and axioms, as well as other theorems.

However, our theorem, the computer, may just be another lemma if we look at a greater scale, like a computer network, that uses multiple computers and even other, new components ethernet cables, routers, etc all put together.

Would this analogy be correct to distinguish between a theorem and a lemma as a matter of scope depending on our end result? Like this: Like Loading Previous Post Aggregating political polls. September 24, at am.

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Notify me of followup comments via e-mail. Written by : Ian. User assumes all risk of use, damage, or injury. You agree that we have no liability for any damages. Summary: 1. Theorems are naturally challenged more than axioms. Author Recent Posts. Latest posts by Ian see all. Help us improve. Rate this post! Ken S.