Definition·D015
Surjective function
A function whose values fill the whole target.
In words
f is surjective onto B exactly when for every y, if y belongs to B then there is some x with x in the domain A and f(x) equal to y: nothing in the target is missed.
Rests onno axioms yet
Never needed: F02 · F03 · F04 · F05 · F06 · F08 · F09 · F10 · F11 · F12 · F13 · F14 · A01 · A02 · A03 · A04 · A05 · A06 · A07 · A08 (computed from the citation graph, not asserted).
Remarks
Surjectivity, unlike injectivity, depends on which target
one has in mind: every function is surjective onto its own range. Cantor's theorem shows a dramatic failure of surjectivity: no function from
to
can be surjective, whatever
is.
Used by
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