Concept in Definition ABC

Theorems are the need and special concern of the mathand when talking about them, reference is made to those statements that can be shown to be true within a logical framework.

Generally, the theorems are composed of a number of conditions that can be listed or anticipated in advance to which they are called responses. Following these, the conclusion or mathematical statement which obviously will always be true in the conditions of the work in question, that is, first of all in the contents informative of the theorem, what will be established is the relationship that exists between the hypothesis and the thesis or completion of work.

But there is something unavoidable for mathematics when a certain statement is plausible to become a theorem and that is that it must be interesting enough within and For the mathematical community, otherwise and unfortunately, it can be simply a motto, a corollary or simply a proposition, and can never become a theorem.

And in order to clarify the issue a little more, it is necessary to also distinguish the concepts that we mentioned above, so that, even then, not being part of a mathematical community we can recognize when it is a theorem, a lemma, a corollary or a proposition.

A Lemma is a proposition, but it is part of a longer theorem. The Corollary for its part is a statement that follows a theorem and finally the proposition is a result that is not associated with any particular theorem.

At the beginning we indicated that a theorem is a statement that can be proved only within a framework logical framework, whereas with logical framework we refer to a set of axioms or axiomatic system and a process of inference which is the one that will allow deriving theorems from the axioms and theorems that have already been derived previously.

On the other hand it will be called demonstration from that theorem to the finite sequence of well-formed logical formulas.

Although not with the special attention that mathematics allocates him to theorems, disciplines such as physics or economy they usually produce statements that are deduced from others and that are also called theorems.