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![[parent]](http://images.planetmath.org:8080/images/uparrow.png) Viewing Correction to 'Schroeder-Bernstein theorem, proof of'
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In the proof of h's surjectivity. by sjs
Correction id: 2955
Filed on: 2003-12-15 03:10:22
Status: Accepted on 2003-12-19 16:02:19
Type: Erratum
Correction text:
In the proof of h's surjectivity,
"Otherwise, $b\in C_k=f(C_{k-1})$ for some $k>1$ ..." should be
"Otherwise, $b\in C_k=f(C_{k-1})$ for some $k\ge1$ ..." or
"Otherwise, $b\in C_k=f(C_{k-1})$ for some $k>0$ ...".
Your recursive definition of $C_k$ is started from 0 (I have decided to use positive integers only in a situation like this since I had often confused whether I started something from 0 or 1).
$f(A)\cap C_0 = \emptyset$ but it can be $f(A)\cap C_1 \not= \emptyset$. Since $B\supset C_1$.
Don't forget $C_1$.
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No comment from object owner mps.
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