Review Note
Last Update: 04/24/2024 02:36 AM
Current Deck: Topology
Published
Fields:
Equivalence 1
Standard definition; \(f\) is left-unique:
\([\forall x_1,x_2 \in X][f(x_1)=f(x_2) \implies x_1=x_2]\)
\([\forall x_1,x_2 \in X][f(x_1)=f(x_2) \implies x_1=x_2]\)
Equivalence 2
The preimage of any element of the codomain has at most one element:
\([\forall y \in Y ][\exists_{\le 1} x\in X] [x \in f^{-1}(y) ]\)
\([\forall y \in Y ][\exists_{\le 1} x\in X] [x \in f^{-1}(y) ]\)
Equivalence 3
\(f\) is an monomorphism/left-cancellative: \(f \circ g = f \circ h \implies g = h\)
Equivalence 4
Equivalence 5
Premise 1
\(f:X\to Y\) is a function
Premise 2
Premise 3
Premise 4
Name
Injective function (3 Definitions)
Context
Set Theory
Subcontext
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