surjective function
- noun
- /sɜrˈdʒɛktɪv ˈfʌŋkʃən/
- Specialized
:
función sobreyectiva
- So the lemma says that if there's a surjective function from the non negative integers to A, then A is countable.
Examples
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For a function to be considered a surjective function, it must cover the entire range of its output set without any gaps.
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In mathematics, a surjective function ensures that every element in the target set is reached by at least one input from the domain.
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To demonstrate a surjective function, you can use the mapping that assigns every real number to its square, showing all positive outputs.
Synonyms
A rule that gives every possible output from some input
A function where every element of the output set has some input that maps to it
Surface Forms
Morphology
The phrase is a transparent compositional combination: 'surjective' names a specific mapping property (every element of the target is hit) and 'function' names the mathematical mapping, so together they mean 'a function that is surjective/onto'. There is no idiomatic or metaphorical shift, so a learner who knows both constituent meanings can derive the MWE's meaning.
Etymology
The term surjective function paints a simple picture: imagine a mail carrier who makes sure every house on a street gets at least one letter. That's why a surjective function means 'onto' — every possible output (house) is reached by at least one input (letter).
