This is a proof, with a visualization via diagram chasing, of a standard exercise about showing that a particular function is surjective (onto). In particular, if f is surjective and the composition g composed with f is injective, then we can show that g is injective. The video includes three "visual definitions" for the terms function, injective, and surjective, and the definitions are utilized when they are needed in the proof. The final proof is written in a way that I think would be acceptable for submission in a class (using words and not symbols and fully justified). Implicit in this explanation is the style of proof required when proving a universal statement (here we use a definition of injective that takes the form of a universal statement followed by a conditional).
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Here is another proof using diagram chasing that function composition is associative: • Function Composition i...
If you are looking for other videos to help with proof writing skills, check out this playlist: • Proof Writing
This animation arose out of a class I am teaching about abstract algebra using the textbook from Tom Judson:
abstract.ups.edu/
#manim #function #injective #surjective #composition #visualmath #math #mtbos #visualproof #settheory #introductiontoproofs #associative #functioncomposition #universalstatement #functiondiagram
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Негізгі бет Function Proof via Diagram Chasing (g composed f injective and f surjective implies g injective).
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