# 1 = 0.999

1 = 0.99999

Algebraic proof -

Let's say x = 0.999999(infinitely)

1 = x (Start with an assumption)

10 = 10x

10 - 1 = 10x - x =9.9999(infinitely) - 0.99999(infinitely) = 9

9 = 9

We haven't reached a Reductio Ad Absurdum so our assumption must have been true, which means that

$\boxed{1 = 0.99(Infinitely)}$

Note by A Former Brilliant Member
1 month, 2 weeks ago

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This is not a right way to prove, there is a way called proof by contradiction, but if from an assumption. If you haven't reached to a contradiction yet this doesn't mean that the assumption was correct. Maybe a contradiction may come out after sometime.

- 1 month, 2 weeks ago

My solution is bad or the Former Brilliant Member's solution is bad?

- 1 month, 2 weeks ago

Former Brilliant Member's solution is bad, because he wanted to explain this

Let $\text{x = 0.999.....}$

$\text{10x = 9.999.....}$

$\text{10x = 9 + 0.999.....}$

$\text{10x = 9 + x}$

$\text{9x = 9}$

$\text{x = 1}$

$\text{1 = 0.999.....}$

but did it in the wrong way

- 1 month, 2 weeks ago

Hahaha! Check this problem :-)

- 1 month, 2 weeks ago

Vinayak used the same Logic. :)

- 1 month, 2 weeks ago

Yeah. What about my solution?

- 1 month, 2 weeks ago

I put a shimmering heart emoji on it as a comment.

- 1 month, 2 weeks ago

Thank you!

- 1 month, 2 weeks ago

Well - what can I do?...

- 1 month, 2 weeks ago

- 1 month, 2 weeks ago

es that yu @Páll Márton because yu Hungarian, are yu youtuber?

- 1 month, 2 weeks ago

No. JustVidman is a famous youtuber in Hungary. He has 629k subscribers and only 15M people speak hungarian so $4\%$. This is equal if he speak in english, then $700M\cdot \frac{629k}{15M}=29M$ subscribers.

- 1 month, 2 weeks ago

Oh, cool!!

- 1 month, 2 weeks ago

😒😕😑😐🤦🤨, @Páll Márton

- 1 month, 2 weeks ago

Seriously? Also, did you see my comment on Did I see something in my dreams? (I)

- 1 month, 2 weeks ago

Can you explain your plans?

- 1 month, 2 weeks ago

I hope you get my plans now.

- 1 month, 2 weeks ago

Sorry! I was just helping my mom.

- 1 month, 2 weeks ago

No worries - I understand. But I hope you now know what I am going to do - problems with them!

First Hexadecimal Clock Problem will be posted today, $13:45$pm

First Binary Clock Problem will be posted tomorrow, $10:30$am

The other two (Algebraic Binary Locks and Algebraic Hexadecimal Locks) will be used later in the summer...

- 1 month, 2 weeks ago

Ok. I'm waiting...

- 1 month, 2 weeks ago

Note - I am using a traditional clock as the base/template for this problem.

- 1 month, 2 weeks ago

I know what is the hexadecimal numbers.

- 1 month, 2 weeks ago

Time's up. The answer is $B:A$ because:

$11 = B, 10 = A$

- 1 month, 2 weeks ago

$1$ minute left.

- 1 month, 2 weeks ago

Let me give you a taster on one of them:

Imagine a clock, but $10, 11, 12$ has been replaced by $A, B, C$.

What's $11:10$ in hexadecimal time?

Give your answer in $5$ minutes.

- 1 month, 2 weeks ago

Yes. $\color{#FFFFFF}\text{some text}$

- 1 month, 2 weeks ago

I upvoted!! :-)

- 1 month, 2 weeks ago

Thank you!

- 1 month, 2 weeks ago

First, i didn't understand why you took 1.8, then I understood, - 1.8 + 0.18 = 1.99. Nice!! Your solution is the best!!

- 1 month, 2 weeks ago

Nice, I never thought of the infinite series like that. Awesome!!

- 1 month, 2 weeks ago