Math Is Fun Forum

Au101

Member

Registered: 2010-12-01

Posts: 353

Looking for confirmation of a proof

Question:

I have an answer to this question, but I'm not confident enough in myself to be certain that this is a valid proof. So I was hoping for some confirmation, or for somebody to tell me why I can't do what I've done. Thanks

Au101

Member

Registered: 2010-12-01

Posts: 353

Re: Looking for confirmation of a proof

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Looking for confirmation of a proof

hi Au101,

That all looks good to me except I would like a bit more to explain this line:

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Au101

Member

Registered: 2010-12-01

Posts: 353

Re: Looking for confirmation of a proof

Yes I puzzled over that. I am sure it is true, because, well I reasoned this out in a few ways I think. First, I thought:

Second I thought:

Which implies, looking at things from the other point of view, that:

And I was about to write that I wasn't sure how to rigorously derive the statement, it just seemed intuitively true to me, but I've now realised that surely my last two lines would do the trick?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Looking for confirmation of a proof

hi Au101,

I thought it was true because these seem like the rules for multiplying powers.

Anyway, thanks for two proofs.  They both look good to me!  Well done!

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob