Proof by Induction


by Bachelier
Tags: induction, proof
Bachelier
Bachelier is offline
#1
Feb1-13, 10:34 PM
P: 376
Is it a solid proof to show that the closure of a union equals the union of the closures of the sets via induction?
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Number Nine
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#2
Feb1-13, 11:24 PM
P: 771
Quote Quote by Bachelier View Post
Is it a solid proof to show that the closure of a union equals the union of the closures of the sets via induction?
How can we possibly know if your proof is valid if you don't show us your proof? Still, I'm not entirely sure why you would use induction here. Are you only considering the union of finitely many sets?
jedishrfu
jedishrfu is offline
#3
Feb1-13, 11:30 PM
P: 2,471
A proof is a proof no matter if you use induction or some direct method as long as the logic of each step is impeccable.

There are some math purists who disdain induction proofs for some theorems and prefer other styles of proof but thats beyond my math understanding to explain here:

http://en.wikipedia.org/wiki/Brouwer...rt_controversy

Bachelier
Bachelier is offline
#4
Feb2-13, 11:22 PM
P: 376

Proof by Induction


Quote Quote by Number Nine View Post
How can we possibly know if your proof is valid if you don't show us your proof? Still, I'm not entirely sure why you would use induction here. Are you only considering the union of finitely many sets?
Yes of course. I'm talking about finite sets. I found a different way to prove it though. But the proof by induction crossed my mind.

I should work it out some time and post it here. It seems feasible.
Bachelier
Bachelier is offline
#5
Feb2-13, 11:22 PM
P: 376
Quote Quote by jedishrfu View Post
A proof is a proof no matter if you use induction or some direct method as long as the logic of each step is impeccable.

There are some math purists who disdain induction proofs for some theorems and prefer other styles of proof but thats beyond my math understanding to explain here:

http://en.wikipedia.org/wiki/Brouwer...rt_controversy
great article. Thanks


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