Lect2 230708501
26
A 2008 A
description
math
Transcript of Lect2 230708501
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Georg Cantor:1845-1918
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I protest above all against the use of an infinite quantity asa completed one§which in mathematics is never allowed.The infinite is only a manner of speaking§in which oneproperly speaks of limits.
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Proof.PC = g[B], h = g ◦ f . 8B½ÂAi , Ci , DiXeµ
A0 = A, C0 = C, D0 = A0 \ C0;An+1 = h[An], Cn+1 = h[Cn], Dn+1 = An+1 \ Cn+1.
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Proof.
-D∗ = A \⋃∞
i=0 Di . �f , gÑØ´÷�§Kk±eäóµé?¿i ≥ 0, Ai+1 ⊂ Ci ⊂ Ai ;D0, D1, · · · , ...üüØ��¶� h(Di) = Di+1.A =
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C =⋃∞
i=1 Di ∪ D∗.
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Proof.½Â¼êk : A → CXeµ
f (a) =
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a, otherwise.
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Proof.
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