If every possible image has at least one variable mapped on it (that is, every element in set B has one or more original images in A), or any element in the range has at least one variable corresponding to it, then this mapping is called surjection.

Let f be the mapping from set A to set B. If all x, y∈A and x≠y have f(x)≠f(y), then f is called injectivity from a to b.

A map that is both injective and surjective is called bijective, also called "one-to-one mapping".

Suppose there is a function about x: y=2x+3. For any x∈R and y∈R, because Y is a linear function of X, there is a unique Y corresponding to any X. By sorting, X=(y-3)/2 can be obtained, so there is also a unique X corresponding to any Y. Thus, y=2x+3 is in the x∈R and y ∈ r domains.

Extended data

In mathematics, injective function is a function that connects different independent variables and different values. More precisely, when the function f is said to be injective, there is at most one x in the definition domain for y in each value domain, so that f (x) = y.

Another way of saying this is that F is injective. When f(a)=f(b), then a=b (if a≠b, then f(a)≠f(b)), where a and b belong to the domain.

The bijection principle is a set of relations. When judging whether an idea can find the only corresponding thing in two directions in application, it is usually necessary to judge whether the idea satisfies the bijective relationship in theory.

Because I don't know the specific way to realize this idea, I need to abstract their relationship and find this bijection. If we can't find it and verify that this bipartite body doesn't exist, then this idea is impossible to realize.

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