Definition: Theorem, Lemma, Proposition, Conjecture and Principle …
Definition: Theorem, Lemma, Proposition, Corollary, Postulate, Statement, Fact, Observation, Expression, Fact, Property, Conjecture and Principle. Most of the time a mathematical statement is classified with one the words listed above. However, I can't seem to find definitions of them all online, so I will request your aid in describe/define them.
What is the role of conjectures in modern mathematics?
2016年11月17日 · Firstly, it is very difficult to overestimate the importance of proofs in mathematics. If you have a conjecture then the only way that you can safely be sure that it is true, is by presenting a valid mathematical proof. The efforts required to prove a conjecture, will require a deeper understanding of the theory in question.
terminology - Difference between axioms, theorems, postulates ...
2010年10月25日 · $\begingroup$ One difficulty is that, for historical reasons, various results have a specific term attached (Parallel postulate, Zorn's lemma, Riemann hypothesis, Collatz conjecture, Axiom of determinacy). These do not always agree with …
combinatorics - Conjecture about crossing paths in $n\times n
2020年5月24日 · Definition to cover a special case just to keep the formulation of the conjecture simple: (1) The top left corner of the grid is defined to belong to the top side and to the left side, and similarly for the other three corners of the grid.
real analysis - What is the difference between lemma, axiom, …
2018年3月31日 · You can use this somewhat interchangably with the word "definition". (You can say this is how you "define" natural or real numbers), but generally a definition goes as: "Defintion: We say a natural number is BOO if it satisfies the following axioms: 1) If you add one to any number which is BOO, the resulting number is not BOO.
discrete mathematics - Confusion on definition of predicate ...
2020年5月21日 · Goldbach’s Conjecture is the statement: "Every even number larger than 2 is the sum of two primes." We can express it using two predicates: "to be a number larger than 2" and "to be the sum of two primes." We can rewrite it in symbolic form using predicate logic.
Create & Prove Conjecture - Discrete Math (Proofs)
2019年5月7日 · Make a conjecture about what totals for points are possible. For example, an employee could not earn 7 points in this scenario. Prove that your conjecture is true. What "conjecture" am I supposed to be making? I assume I am trying to find a fact/pattern; something like "points can only be obtained in multiples of 6", but I am lost. I only ...
Terminology: Difference between Lemma, Theorem, Definition, …
2015年4月23日 · Once it is proven or disproven, it ceases to be a conjecture and either becomes a fact (backed by a theorem) or there is some interesting counterexample to demonstrate how it is wrong. Example: The Poincar$\acute{\text{e}}$ conjecture was a famous statement that remained an open research problem in topology for roughly a century.
A weak form of the abc conjecture involving the definition of …
2020年4月28日 · I wondered about a weak form of the abc conjecture, see the Wikipedia abc conjecture using the theory of generalized means, I mean this Wikipedia Generalized mean. We get the following claim, where $\\
ABC-conjecture: is the 3rd definition in Wikipedia really valid?
2020年4月12日 · In fact, this third form of the conjecture is directly equivalent to the first form via taking logarithms. What this calculation does show, though, is that if the conjecture is true, then $3^n$ and $2^k$ usually don’t get very close and their difference is usually not highly factorizable. Here’s Java code that calculates the quality up to ...