Math name for asymetric-pair relationship?

In summary, the conversation discusses the concept of an "asymmetric-pair" relationship in mathematics, where one function cannot be inverted to reconstruct its input, but another function can. This idea is commonly used in public key encryption and has a general mathematical interpretation. Examples of such pairs of functions do exist, such as the functions f(x) = tan(x) and g(x) = arctan(x).
  • #1
Mr Peanut
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Math name for "asymetric-pair" relationship?

Say I have a function (F) that takes an input (P) and returns an output (E). Suppose F isn't invertible so, knowing F and E, one could not reconstruct P.

Suppose also that there is another function (R) that can take E as input and returns P... without any prior knowledge about P other than it was generated with F. (R could also be non-invertible but need not necessarily be.)

I know the computer people refer to an imperfect, practical application of this idea as public key encryption or asymmetric encryption. It assumes that prime number factors for large numbers cannot be determined analytically in practical time.

But the concept has a perfect, general, underlying mathematical interpretation.

1) Does mathematics have a name for such a pair of functions?

2) Could they, in fact, exist?

3) If they do exist; are there any examples?
 
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  • #2


If I'm not mistaken, R is a left inverse of F since, as you've defined it,
[tex]
R(F(P)) = R(E) = P
[/tex]
for any P in the domain of F. Therefore [itex] R \circ F = \text{id}[/itex].

For an easy example, consider the functions [itex] f(x) = \tan(x)[/itex] and [itex]g(x) = \arctan{x}[/itex] defined on the reals. Then [itex] f(g(x)) = x[/itex] but [itex] g(f(x))= x+2 \pi n[/itex].
 

1. What is an asymetric-pair relationship in math?

An asymetric-pair relationship in math refers to a relationship between two variables where one variable's value is not dependent on the value of the other variable. This means that the relationship is not symmetric, as the values of the two variables do not have a direct influence on each other.

2. How is an asymetric-pair relationship represented mathematically?

In mathematical notation, an asymetric-pair relationship is typically shown as y = f(x), where the value of y is determined by a function of the value of x. This indicates that x is the independent variable and y is the dependent variable.

3. What is an example of an asymetric-pair relationship in real life?

An example of an asymetric-pair relationship in real life is the relationship between a person's age and their income. While a person's age may increase over time, their income may not necessarily increase at the same rate or be directly dependent on their age.

4. How is an asymetric-pair relationship different from a symmetric relationship?

An asymetric-pair relationship differs from a symmetric relationship in that a symmetric relationship involves two variables that have a direct and reciprocal influence on each other. In a symmetric relationship, the value of one variable can be determined by the value of the other variable, whereas in an asymetric-pair relationship, this is not the case.

5. What is the importance of understanding asymetric-pair relationships in math?

Understanding asymetric-pair relationships in math is important because it allows us to accurately model and analyze real-life situations, where variables may not have a direct and equal influence on each other. It also helps in identifying and predicting patterns and trends in data, which can be useful in making informed decisions and solving problems.

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