Understand the subject
What makes a finite mapping a function?
A function assigns each domain element exactly one codomain image. Injection and surjection describe extra one-to-one or onto properties.
Use it to classify an entered mapping before calling it a bijection.
See the structure
What the rule checks
a → 1b → 2bijective ⇔ injective and surjective
Worked interpretation
Read the result in context
{(a,1),(b,2)} from {a,b} to {1,2} is bijective.
Interpret with care
Important boundary
A missing domain input or two outputs for one input means the relation is not a function.
Use the Set Operations Calculator to explore small finite examples.
Quick guide
How to use this calculator
- Enter values using the notation shown beside each field.
- Choose a calculation mode when the tool offers more than one interpretation.
- Read the primary answer first, then inspect the supporting details.
Calculation method
Apply the stated definition
Every domain element must have exactly one image.
The calculator validates the mathematical domain before returning a result and does not replace undefined states with zero.
Worked example
Worked example
{(a,1),(b,2)} from {a,b} to {1,2} is bijective.
Every domain element must have exactly one image.
Supported inputs
Precision and limits
Finite, bounded input
Set and logic tools use finite inputs so every result can be checked completely. Each page states its practical size limit.
Notation
Set elements are comma-separated text labels. Logic operators and relation-pair notation are documented in the relevant input labels.
