0.9² = 0.81
0.99² = 0.9801
0.999² = 0.998001
0.9999² = 0.99980001

The more 9s go on the end, the more 9s go into the answer. Tend to infinity and you get an infinite number of 9s in the answer, so (0.9...)² = 0.9...

This is perfectly inline with 0.9... equaling 1, since 1² equals itself too. Further, you can show through other methods that 0.9... is equal to 1, thus any complaint about the square not being 1 is fallacious.

Same method works with other numbers. For instance, we know that from the 0.9... = 1 proof, that 1.9... = 2, and that 3.9... = 4.

(1.9...)² = 3.9...

This calculation is exactly what we should expect since it is the same as 2² = 4.

Is it just me or is the same thing being said over and over unto no ends? Kind of ironic considering the subject matter of the thread.

It is a vicious echo and yet hypnotically entertaining!

Rhizo

The same thing is being said, but in different ways and with different proofs...for those who still don't "get" it.

(October 20, 2009 at 4:16 am)Tiberius Wrote: The same thing is being said, but in different ways and with different proofs...for those who still don't "get" it.

At least Sae has given up.

What is the best way you know of to explain the proof verbally Adrian? I tried showing some classmates the mathematical proof today but they couldn't follow.

I guess the best verbal one would be to ask them to think of a number which can fit between 0.9... and 1. Then again, the proof for that is also mathematical, so I'm not sure if it would work verbally

The best mathematical proof is usually the 1/3 one, since most people can do long division, and then it's just a case of multiplying by 3, which people can do as well.

I think the most elegant proof is the infinite series one though.

(October 20, 2009 at 5:10 am)theVOID Wrote: At least Sae has given up.

I get it - I did a long time ago. What is it with you people and not wanting to think about stuff??

Thinking about stuff is good. It's just not usual for someone to try and come up with a load of contradictions to something they know is proven. Do you just like watching me mathematically destroy them?

You are such a pedant Adrian. One lil mistake and you dance like a fairy. Let me bow and worship your fukking big fat head a bit...

Right, that's better

Like I said, I find the subject interesting. If you don't want to discuss it then don't.

I discovered another proof.

1/9=0.1r

1/9+0.9r=1.1r bcause all the 1s added to the 9swill make the 1s go forward.

Hence 0.9r=1