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- Jun 22, 2012

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The two books are as follows:

"Functions of a Complex Variable I" (Second Edition) ... by John B. Conway

"Complex Analysis for Mathematics and Engineering" by John H. Mathews and Russel W. Howell (M&H) [Fifth Edition] ...

Conway's proof that for a function of a complex variable, differentiability implies continuity ... reads as follows:

Mathews and Howell's proof that for a function of a complex variable, differentiability implies continuity ... reads as follows:

Now, as can be seen in the above proofs, Conway uses modulus/norm signs around the expressions in the proof while Mathews and Howell do not ...

Can someone explain the differences ... are both correct ... ?

Surely the Conway proof is more valid as the proof involves limits which involve ideas like "close to" which need modulus/norms ...

Hope someone can clarify this issue ...

Peter