Restriction (mathematics)

In mathematics, the concept constraint is usually used for the reduction of the domain of a function.

Also, it is possible for relations to consider the restriction to a subset of the ground set.

Occasionally the phrase " without loss of generality " ( without loss of generality ) is used in mathematical proofs. This has nothing to do with the mathematical concepts discussed herein.

• 2.1 Example

Restriction of a function

Definition

Is an arbitrary function, and a subset of the defined amount, then is meant by the restriction of function to that which matches up with. With the inclusion mapping can write short stint as the

In the situation is also called a sequel. In set theory, the notation is used instead.

Example

Be the set of real numbers and the square function. is not injective, the restriction to the interval of non-negative real numbers, but this is already. If you also the target quantity to the image set ( also ) restricts, obtained with the bijective quadratic function therefore has an inverse function, namely, the square root function.

Restriction of a relation

R is a binary relation on the amount of A and X a subset of A, then the ratio X is S to the limitation of R to X, when A and B is valid for all of X:

Example

The less-than relation on the set of integers is the restriction of small - relation on the set of rational numbers.

• Mathematical function
• Set theory