Definitions
- Describing a mathematical function that is both injective and surjective. - Referring to a one-to-one correspondence between two sets. - Talking about a function that has a unique input for every output and vice versa.
- Describing a mathematical function that maps distinct inputs to distinct outputs. - Referring to a function where different inputs never produce the same output. - Talking about a one-to-one function that preserves distinctness of elements.
List of Similarities
- 1Both terms are used in mathematics.
- 2Both describe properties of functions.
- 3Both involve mapping inputs to outputs.
- 4Both ensure distinctness in the relationship between inputs and outputs.
What is the difference?
- 1Definition: Bijective refers to a function that is both injective and surjective, while injective only refers to a function that maps distinct inputs to distinct outputs.
- 2Uniqueness: Bijective guarantees a unique input for every output and vice versa, while injective only guarantees distinctness of inputs.
- 3Surjectivity: Bijective includes surjectivity as a requirement, while injective does not consider the range of the function.
- 4Inverse: Bijective functions have an inverse function that maps outputs back to inputs, while injective functions may not have an inverse function.
- 5Cardinality: Bijective functions establish a one-to-one correspondence between sets of the same size, while injective functions do not necessarily have this property.
Remember this!
Bijective and injective are terms used in mathematics to describe properties of functions. While both terms involve mapping inputs to outputs and ensuring distinctness, the difference lies in their definitions and requirements. A bijective function is both injective and surjective, guaranteeing a unique input for every output and vice versa. On the other hand, an injective function only maps distinct inputs to distinct outputs, without considering the range or surjectivity of the function.
