onto function
- noun
- /ˈɒntu ˈfʌŋkʃən/
- Specialized
:
función sobreyectiva
- An onto function maps every element of its codomain.
Examples
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A onto function guarantees that the codomain has no unused elements.
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To prove the mapping is an onto function, we must show that every output is achievable.
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Every onto function from a set with two elements to itself is also one-to-one.
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Is this an onto function or a one-to-one function?
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An onto function ensures that for every output value, there is at least one input that maps to it.
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In mathematics, an onto function is often characterized by its ability to achieve every possible output in the codomain.
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To validate that a function is an onto function, each element in the codomain must be linked to at least one element in the domain.
Synonyms
A rule that gives every output value at least one input value
A function where every element of the output set has some input that maps to it
Surface Forms
Morphology
The meaning is directly compositional: 'onto' (given here as meaning 'surjective') modifies 'function' to indicate a function that covers its codomain, so the overall sense is predictable from the parts. Although this is technical vocabulary, the adjective+noun construction follows regular English composition and would be transparent to learners who know the technical sense of 'onto'.
Etymology
Onto function uses onto in the sense of 'landing on' and function as a mapping, so imagine throwing pebbles and every target stone gets a pebble — nothing in the target area is left without a hit. So an onto function means 'every possible output' is produced by at least one input.
