master > master: Formattierung
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@ -127,20 +127,21 @@ V = lin{v1, v2, v3}
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## UB9-3 (wie man ansetzen kann...) ##
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ZZ ψ◦ϕ injektiv <===> ϕ injektiv + Kern(ψ) ∩ Bild(ϕ) = {0}
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**Zz:** ψ◦ϕ injektiv <===> ϕ injektiv + Kern(ψ) ∩ Bild(ϕ) = {0}
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(==>) Angenommen, ψ◦ϕ injektiv.
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Zz: ϕ injektiv + Kern(ψ) ∩ Bild(ϕ) = {0}.
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**Zz:** ϕ injektiv + Kern(ψ) ∩ Bild(ϕ) = {0}.
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...
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(<==) Angenommen, ϕ injektiv + Kern(ψ) ∩ Bild(ϕ) = {0}.
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Zz: ψ◦ϕ injektiv
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**Zz:** ψ◦ϕ injektiv
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Laut Korollar 6.3.15 aus [Sinn2020] reicht es aus zu zeigen, dass Kern(ψ◦ϕ) = {0}.
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Laut Korollar 6.3.15 aus [Sinn2020] reicht es aus zu zeigen,
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dass Kern(ψ◦ϕ) = {0}.
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Sei x ∈ U beliebig.
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Zz: x ∈ Kern(ψ◦ϕ) <===> x = 0
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**Zz:** x ∈ Kern(ψ◦ϕ) <===> x = 0
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x ∈ Kern(ψ◦ϕ)
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<===> (ψ◦ϕ)(x) = 0
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