# Proof that a power series equals zero for all z iff each coefficient is zero

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• Feb 25th 2010, 06:52 PM
davismj
Proof that a power series equals zero for all z iff each coefficient is zero
http://i49.tinypic.com/29qjok8.jpg

I didn't quote a lot of theorems here because they all seem pretty trivial. Is this a sufficient proof? (Please note: I'm sure there are better ways to prove this, but I'm most interested in whether or not I'm formulating good/sufficient/test-worthy proofs). Thanks so much! (Bow)
• Feb 25th 2010, 06:58 PM
Drexel28
Quote:

Originally Posted by davismj
http://i49.tinypic.com/29qjok8.jpg

I didn't quote a lot of theorems here because they all seem pretty trivial. Is this a sufficient proof? (Please note: I'm sure there are better ways to prove this, but I'm most interested in whether or not I'm formulating good/sufficient/test-worthy proofs). Thanks so much! (Bow)

I would agree with that!
• Feb 25th 2010, 07:10 PM
davismj
Quote:

Originally Posted by Drexel28
I would agree with that!

Finally, I got one! You don't know how long I've been waiting for this!