Theorem


The word Theorem comes from the Latin theorēma, it is not an obvious truth, but it is demonstrable. Theorems arise as a result of intuitive properties and are exclusively deductive in nature, for which a type of logical reasoning (demonstration) is required to be accepted as absolute truths.

Some examples of theorem are the following: the square of the sum of the hypotenuse is equal to the sum of the squares of the legs. If a number ends in zero or five, it is divisible by five.

In the postulates (intuitive truth with enough evidence to be accepted as such) as in the theorems there is a conditional (hypothesis) and a conclusion (thesis) that is considered to be fulfilled in case the conditional part or hypothesis is valid. Demonstration is required in theorems, which is nothing more than a series of concatenated arguments that are based on postulates or on other theorems or laws already demonstrated.

It is very important to take into account the reciprocity of a theorem. This becomes another theorem whose hypothesis is the thesis of the first (direct theorem) and whose thesis is the hypothesis of the direct theorem. For example:

Direct theorem, if a number ends in zero or five (hypothesis), it will be divisible by five (thesis).

Reciprocal theorem, if a number is divisible by five (hypothesis), it has to end in zero or five (thesis). You have to be very careful because the reciprocal theorems are not almost always true.

Some of the most famous theorems in history are: Pythagoras, Thales, Fermat, Euclid, Bayes, the central limit, prime numbers, Morley, among others.