Logical coherence is called congruence.
Congruence , from the Latin congruentia , is coherence or logical relationship . It is a characteristic that is understood from a link between two or more things.
For example: “It is inconsistent that you want to give a gift to the person with whom you are in legal litigation,” “The judge detected several inconsistencies between the defendant's statements and the evidence,” “Each part of this system is consistent with the others.”
Mathematical congruence
For mathematics , congruence is the algebraic expression that expresses the equality of the remainders of the divisions of two congruent numbers by their module (a natural number other than 0). This expression is represented with three horizontal lines between the numbers and, if we assign them the variables a and b , it is read as follows: a is congruent with b modulo m .
Mathematical congruence, therefore, refers to two integers that have the same remainder when divided by a natural number other than zero (the module ) .
Fermat's little theorem
On the other hand, for mathematical identity , the concept of congruence can refer to Fermat's little theorem (one of the most prominent in relation to divisibility), which presents the following formula: if we have the prime number p , then for everything natural number a it is given that a to the power of p is congruent with a modulo p .
This same theorem is usually presented in another way, although both formulas are equivalent: if we have the prime number p , then for all a , a natural number prime relative to p , a to the power of p -1 is congruent with 1 module p . In other words, if we subtract a from the result of raising said number to p , we obtain a number divisible by p .
At the judicial level, coherence is linked to the conformity between the claims of the parties and the pronouncements of a ruling.
Equations and congruence
Furthermore, the term congruence is used to express an equation with at least one unknown; In this case, the aim is to know if there is a solution, or more than one.
It is worth mentioning that several of the properties of congruence are also found in equality; Let's look at some examples:
* when the modulus is fixed, congruence represents an equivalence, since it is possible to check reflexivity ( a is congruent with a modulo m), symmetry (if a is congruent with b modulo m , then b is congruent with a modulo m ) and transitivity (if a is congruent to b modulo m and b is congruent to c modulo m , then a is congruent to c modulo m );
* if a is relatively prime with m and a is congruent with b modulo m , then it is correct to say that b is relative prime with m ;
* If a is congruent with b modulo m and we have an integer k , then it is correct to state that: the sum of a and k is congruent with the sum of b and k modulo m ; the product of k and a is congruent with the product of k and b modulo m ; a to the k is congruent with b to the k modulo m , as long as k is greater than 0.
Congruence between polygons , on the other hand, is the one-to-one correspondence between their vertices such that the angles are congruent (that is, they have the same measurement), as are their sides (they have the same length).
The term in law and religion
In the field of law , congruence is the conformity between the pronouncements of a ruling and the claims that the parties had formulated during the trial .
As a rational method of conflict resolution, the judicial process must achieve agreement between the claim of the plaintiff, the opposition of the defendant, the evidence and the court's decision. This agreement is what is known as congruence.
In religion , finally, congruence is the effectiveness of God 's grace, with its ability to act without interfering with the freedom of the human being.