The word Theorem comes from the Latin theorēma, it is not an obvious truth, but it is demonstrable. The theorems arise as a result of intuitive properties and are exclusively deductive in nature, which is why a type of logical reasoning (proof) is required to be accepted as absolute truths.
Some examples of the 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), such as 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. The theorems require the proof, which is nothing more than a series of concatenated reasonings that are supported by postulates or other theorems or laws already proven.
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 vigilant because reciprocal theorems are not almost always true.
Some of the most famous theorems in history are: Pythagoras', Thales, Fermat, Euclides, Bayes, the central limit, prime numbers, Morley, among others.
