(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove that [tex]\forall[/tex] f:X[tex]\rightarrow[/tex]Y there [tex]\exists[/tex] Z, h: X[tex]\rightarrow[/tex]Z is injective and g: Z[tex]\rightarrow[/tex]Y is surjective, so that f=g*h.

2. Relevant equations

There is already a conclusion from the factorisation theorem of functions that: [tex]\forall[/tex] f:X[tex]\rightarrow[/tex]Y there [tex]\exists[/tex] Z, h: X[tex]\rightarrow[/tex]Z is surjective and g: Z[tex]\rightarrow[/tex]Y is injective, so that f=g*h.

But how to prove it just from applaying it from other side..

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# Homework Help: Conclusion from the factorization theorem of functions.

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