bijective

Examples of bijective in the following topics:

• Counting Rules and Techniques

  • Bijective proofs are utilized to demonstrate that two sets have the same number of elements.
  • A bijective proof is a proof technique that finds a bijective function $f: A \rightarrow B$ between two finite sets $A$ and $B$, which proves that they have the same number of elements, $|A| = |B|$.
  • A bijective function is one in which there is a one-to-one correspondence between the elements of two sets.
  • If $B$ is more easily countable, establishing a bijection from $A$ to $B$ solves the problem.

• Line Integrals

  • where $r: [a, b] \to C$ is an arbitrary bijective parametrization of the curve $C$ such that $r(a)$ and $r(b)$ give the endpoints of $C$ and $a$.
  • where $\cdot$ is the dot product and $r: [a, b] \to C$ is a bijective parametrization of the curve $C$ such that $r(a)$ and $r(b)$ give the endpoints of $C$.