proof .999=1

[meli123]

heyyy guysss....just trying to make a code to proove .999=1

any ideass?? :))
ty!!

[Moschops]

I'm not sure that code can prove it; you're asking the machine to deal with numbers to infinite precision. As soon as you start hitting floating point limits, you can no longer trust the numbers.

[Eagletalon]

.round?

[murnesty]

If you want to make 0.999 become 1 then you use ".round ". Else f you want prove it mathematically then try this http://en.wikipedia.org/wiki/Limit_(mathematics). Write your code for this equation. I never try. XD

[TrustyTony]

In my computer it takes 16 iterations from 0.9 to reach floating point limit of accuracy, if you mean that:

1 0.99
2 0.999
3 0.9999
4 0.99999
5 0.9999990000000001
6 0.9999999
7 0.9999999900000001
8 0.999999999
9 0.9999999999
10 0.99999999999
11 0.999999999999
12 0.9999999999999001
13 0.99999999999999
14 0.999999999999999
15 0.9999999999999999
16 1.0

The code was not in C++, but results should be similar in C++.

[mrnutty]

Idk if this works but maybe try out using this algebra:

1/9 = 0.1111....
9 * 1/9 = 9 * 0.1111
1 = 0.999....

See if you get similar result on a computer.

[Anirudh Rb]

No code can do that..it's a totally crazy idea. I'd love to know if you find a way to do that.

[doug65536]

Not sure how you plan to write a program to prove that, since you already know it's false.

[TrustyTony]

No it is True with repeating decimal 9 of infinite precicion see previous post proving it simply and elegantly with 1 / 9 *9 (same could be done with decimal reprecentation of any number with inverse with repeating decimals)

[NicAx64]

I'm not sure are you looking this?

LHS= .9999*
= ( 1.0 - 0.0*****1 )
= 1.0 - lim[n->infinity] 1/n
= 1.0 - 0
= 0

.: LHS = RHS

so proving this using code is simple. So you need a Automated Theorm Proving
math engine and in font end you can fetch the following rules.

[Nick Evan]

Here's a nice video about it, which I recently stumbled upon.

[doug65536]

I didn't see anything saying that the OP was asking to prove that 0.999<repeating> was equal to 1.0. The OP says, prove that 0.999 (which I interpreted as exactly 0.999 as in 0.999000).

Is this a sinister puzzle given by a computer science teacher or something? If so, I believe I see the trick to it.

The puzzle probably wants you to realize that floating point numbers are typically stored with a mantissa and an exponent. What I believe the puzzle is looking for is you to come up with a floating point representation format where the mantissa doesn't have enough bits to store 0.999 - the closest representation would be 1.0.