Does .9-repeating equal 1?

[Combat Ingrid]

Originally posted by -Jrabbit
the exact number for pi

http://pi.ytmnd.com/

[SlowwHand]

Denim blue. Periwinkle is nice in it's proper use.

[Combat Ingrid]

255,255,255 power!

[Elok]

So? The question's still silly. If .999... is 1, then in all projects where we would add/subtract/divide/multiply another number by .999... we would just do so by one.

If, on the other hand, we think they are not equal, when confronted by such a problem we will either round up to one or spend the rest of our lives pressing the 9 key on our calculators trying to express infinity. I am not aware of any system of numbers under which 9 is closer to zero than to ten, so basically the only choice is to work with one instead of the decimal, or else to accept less accurate results in our mathematical operations by rounding down to a finite decimal.

So, no matter which end you start from, you're eating the same egg.

[Heresson]

Two real numbers are identical if and only if their (absolute) difference is not equal to a positive (third) real number. Given any positive value, the difference between 1 and 0.999… is less than this value (which can be formally demonstrated using a closed interval defined by the above sequence and the triangle inequality). Thus the difference is 0 and the numbers are identical

Proofs of 1/3 = 0,333(...) is not logical. Attitude of 1/3 and 0,333(...) is exactly as 1 and 0,999(...), so if someone questions the proposition 1=0,999(...), he has to question 1/3=0,333(...) as well.

The quoted part rests on theory of real numbers.

Of course, 0,000(n)1 is a logical fallacy, if we accept the concept of infinity, because there always is one more 0 to add.
We can not define the difference between 0,999(...) and 1. But does it make it the same?

[KrazyHorse]

Yes, actually.

[KrazyHorse]

Either that or you might as well throw away all of calculus. I'd rather keep things the way they are, thanks.

[Spec]

Originally posted by KrazyHorse


You could probably do it (it/s been 5 years since my last analysis class). But I was talking to GP.

Anyhow, your answer is obviously correct (by the definition and existence of transcendentals)

Sure. Like I said, it depends on the application.

Example. Lets say a comet is 300000 light years away from the earth and almost heading right twords it. For it to hit a bullseye. you have to make it turn one degree to the left. At that distance, 0.9999 might just be enough for a miss.

.9999 is not 1.

Spec.

[LordShiva]

What?

[Pekka]

I think we should also.. the space mission is important, right? SO we need to guarantee that the mission will represent our values and our mankind as a whole. Comprhenesive approach to the new frontier.

We need people in NASA, ESA etc, who disagree with this thing. But I'm not flying that baby See the little bugger go 'WOoooouuuuuuuuuuuuuuuuuuuu* and miss the target. Is this MARS daddy? No, this is us blowing before we even get off the ground son! Send your greetings to '.9999 truth comission' club!

[Spec]

A change of one degree or .9999 degree in a trajectory 3000000 light years away makes a big difference, so, 1 is not .9999.

Spec.

[LordShiva]

Noone's saying it is.

[RGBVideo]

Example. Lets say a comet is 300000 light years away from the earth and almost heading right twords it. For it to hit a bullseye. you have to make it turn one degree to the left. At that distance, 0.9999 might just be enough for a miss.

.9999 is not 1.

correct

0.9999... on the other hand, clearly is 1. You'll realize that yourself once you read this post. Start from the first x, stop just before QED. Now what part of the equations did you not understand?

[KrazyHorse]

Originally posted by Spec


Sure. Like I said, it depends on the application.

Example. Lets say a comet is 300000 light years away from the earth and almost heading right twords it. For it to hit a bullseye. you have to make it turn one degree to the left. At that distance, 0.9999 might just be enough for a miss.

.9999 is not 1.

Spec.

0.9999 is not 1

0.9999... means that you have an infinite string of 9s

IN-FI-NITE

Ever and anon, world without end, amen.

0.9999... is 1

Not for all intents and purposes, not to x degree of accuracy. In standard decimal representation they represent the same number. This is not an approximation. There is no error associated with it. They are mathematically interchangeable.

In the name of Cantor, Leibniz and Russell, amen

[Pekka]

What KH said. But really, this has been said multiple times and we are facing a situation where people would rather choose what they believe in. This setting is not sustainable, so it is useless to.. debate about it.