Difference between revisions of "Talk:Aufgaben:Problem 14"
From Ferienserie MMP2
Line 1: | Line 1: | ||
What should this "Pierre's lemma" be? It's clearly false: | What should this "Pierre's lemma" be? It's clearly false: | ||
− | Let \( f = u + iv \) (with \( u \) and \( v \) real-valued) be any non-constant analytic function; then clearly \( u \) or \( v \) is not constant. Following "Pierre's lemma" they should both be analytic, but we've showed in Ch. II.3 that any analytic real-valued function | + | Let \( f = u + iv \) (with \( u \) and \( v \) real-valued) be any non-constant analytic function; then clearly \( u \) or \( v \) is not constant. Following "Pierre's lemma" they should both be analytic, but we've showed in Ch. II.3 that any analytic real-valued function is constant, which is a contradiction. |
(And in any case, in the "proof" \( a \) and \( b \) should be different from \( 0 \)...) | (And in any case, in the "proof" \( a \) and \( b \) should be different from \( 0 \)...) | ||
Cheers, the tables | Cheers, the tables |
Revision as of 13:45, 31 December 2014
What should this "Pierre's lemma" be? It's clearly false: Let \( f = u + iv \) (with \( u \) and \( v \) real-valued) be any non-constant analytic function; then clearly \( u \) or \( v \) is not constant. Following "Pierre's lemma" they should both be analytic, but we've showed in Ch. II.3 that any analytic real-valued function is constant, which is a contradiction. (And in any case, in the "proof" \( a \) and \( b \) should be different from \( 0 \)...)
Cheers, the tables