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

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

Easy Math Editor

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Math	Appears as
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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
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Comments

Hahaha! Check out this problem :-)

A Former Brilliant Member - 11 months, 3 weeks ago

Vinayak used the same Logic. :)

A Former Brilliant Member - 11 months, 3 weeks ago

Yeah. What about my solution?

A Former Brilliant Member - 11 months, 3 weeks ago

@A Former Brilliant Member – Nice, I never thought of the infinite series like that. Awesome!!

A Former Brilliant Member - 11 months, 3 weeks ago

@A Former Brilliant Member – I upvoted!! :-)

A Former Brilliant Member - 11 months, 3 weeks ago

@A Former Brilliant Member – Thank you!

A Former Brilliant Member - 11 months, 3 weeks ago

@A Former Brilliant Member – 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!!

A Former Brilliant Member - 11 months, 3 weeks ago

@A Former Brilliant Member – I put a shimmering heart emoji on it as a comment.

A Former Brilliant Member - 11 months, 3 weeks ago

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.

Zakir Husain - 11 months, 3 weeks ago

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

A Former Brilliant Member - 11 months, 3 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

A Former Brilliant Member - 11 months, 3 weeks ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$