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If 𝑔 ∘ 𝑓 is one-to-one, then 𝑓 is one-to-one
Автор: Dogmathic
Загружено: 2025-08-18
Просмотров: 333
Описание:
In this video, we prove that for functions f and g, where f is from the set A to B and g from B to C, if g composed of f is one-to-one (injective), then the function f is one-to-one (injective). We prove this directly by using the definition of one-to-one.
Chapters:
00:00 Introduction
00:34 Definition of One-to-One / Injective
02:17 Function and Composition Graph
03:10 Proof
06:34 QED and Thanks for Watching
#discrete_mathematics #discrete #topology #pointsettopology #analysis #abstractalgebra #functions #onto #surjectivefunction #onetoone #injectivefunction
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