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Proof

(related to Corollary: Set Difference and Set Complement are the Same Concepts)

• Assume, the set complement $B^C$ was an "absolute complement".
• This would mean that the set union $B^C\cup B$ would contain all sets.
• This is a contradiction to a previously proven corollary of the axiom of separation.
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References

Bibliography

1. Hoffmann, Dirk W.: "Grenzen der Mathematik - Eine Reise durch die Kerngebiete der mathematischen Logik", Spektrum Akademischer Verlag, 2011
2. Ebbinghaus, H.-D.: "Einführung in die Mengenlehre", BI Wisschenschaftsverlag, 1994, 3th Edition