I have an intuitive understanding of the definitions that will follow,

[Noxide]

I have an intuitive understanding of the definitions that will follow, but in my search to find specific definitions I only come up with vague explanations and contentious or subjective uses of those definitions. Please provide some definitions (mathematical) for the following list (and sources if possible):

proposition

lemma

corollary

theorem

principle

law

ruleThanks

 

[_DJ_british_?]

proposition

http://en.wikipedia.org/wiki/Proposition"

lemma

http://en.wikipedia.org/wiki/Lemma_%28mathematics%29"

corollary

http://en.wikipedia.org/wiki/Corollary"

theorem

http://en.wikipedia.org/wiki/Theorem"

principle

http://en.wikipedia.org/wiki/Principle"

law

http://en.wikipedia.org/wiki/Scientific_law"

rule

http://en.wikipedia.org/wiki/R.U.L.E."

 

[Noxide]

Many of the definitions listed depend on the definition of a proposition, however according to wikipedia (which I am aware of) there exists a great deal of contention as to the definition of a preposition...

 

[_DJ_british_?]

Last sentence in the introduction of the "proposition" article : "Strawson advocated the use of the term "statement" (instead of proposition), and this is the current usage in mathematical logic."

Here.

 

[CellCoree]

for your question! I understand the importance of clear and precise definitions in order to accurately communicate and understand concepts. Below are some definitions for the terms you have listed, along with their sources:

1. Proposition: A statement that is either true or false, but not both. It is used as a building block for logical arguments and proofs. (Source: "Proposition." Merriam-Webster Dictionary.)

2. Lemma: A proven statement or theorem that is used as a stepping stone to prove a larger result. It is considered a smaller, less significant result compared to a theorem. (Source: "Lemma." Oxford Dictionary of Mathematics.)

3. Corollary: A result that follows directly from a theorem or proposition. It is usually a simpler or more specific version of the original statement. (Source: "Corollary." Oxford Dictionary of Mathematics.)

4. Theorem: A statement that has been proven to be true using rigorous mathematical reasoning and logical arguments. It is considered a significant result in mathematics. (Source: "Theorem." Merriam-Webster Dictionary.)

5. Principle: A fundamental truth or assumption that serves as a basis for reasoning or a system of beliefs. In mathematics, it refers to a fundamental concept or rule that is used to guide problem solving. (Source: "Principle." Oxford Dictionary of Mathematics.)

6. Law: A statement that describes a relationship or pattern observed in nature. In mathematics, it refers to a general rule or principle that is used to describe a mathematical concept or phenomenon. (Source: "Law." Oxford Dictionary of Mathematics.)

7. Rule: A specific procedure or guideline that must be followed to solve a problem or reach a specific result. In mathematics, it refers to a specific mathematical operation or procedure. (Source: "Rule." Oxford Dictionary of Mathematics.)

I hope these definitions provide you with a clearer understanding of these terms. It is important to note that some of these terms may have slightly different meanings or interpretations depending on the context in which they are used. Therefore, it is always best to consult reliable sources and use precise language in mathematical discussions.