Proof by Induction: Closure of Union = Union of Closures

[Bachelier]

Is it a solid proof to show that the closure of a union equals the union of the closures of the sets via induction?

 

[Number Nine]

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]

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 that's beyond my math understanding to explain here:

http://en.wikipedia.org/wiki/Brouwer–Hilbert_controversy

 

[Bachelier]

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]

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 that's beyond my math understanding to explain here:

http://en.wikipedia.org/wiki/Brouwer–Hilbert_controversy

great article. Thanks