Does .9-repeating equal 1?

[RGBVideo]

Of course it does. I can't believe people could disagree with this.

You take 1 and divide it by 3, you get .3 repeating indefinitely. Multiply by 3, and you get .9 repeating indefinitely. Which equals 1.

this is a circular argument, you write this to a maths test asking you to prove 0.9... = 1 and you'll receive 0 points unless you write a separate proof that 1/3 = 0.3...

Originally posted by Park Avenue
No. That extra 0.0001 makes all the difference you know.

yes, and given that there are an infinite number of 0's before the 1, 10 - 9.9... = 0.

edit:
[quote]

Originally posted by Ben Kenobi
They aren't the same.

n(n)^x where n is 1 is always one.

lim x -> inf will be 1.

What is the value for

n(n)^x where n is 0.9 repeater?

what about the lim x -> inf? that should be 0.

trolling?

[LordShiva]

But what about repeating 10s?

[Provost Harrison]

You know, this would be quite a pleasant mathematics thread, if it wasn't for the fact that some of the posters here are so f**king arrogant...

[Pekka]

To answer to the question of the topic, yes it equals 1.

Very basic mathematics. Been shown here already also.

It's not a matter of belief. It's a matter of mathematial facts. DO we have a single math student here or student who has taken more than one course of math that actually disagrees with this statement? It's like one of those universal things that everyone knows.

[Pekka]

Originally posted by Ben Kenobi
They aren't the same.

n(n)^x where n is 1 is always one.

lim x -> inf will be 1.

What is the value for

n(n)^x where n is 0.9 repeater?

what about the lim x -> inf? that should be 0.

Uhm?

lim where n->inf 0.999999 = lim n->inf (1 - 1/10^n)

= 1 - lim n-> inf 1/10^n ................... = 1.

[Eli]

Originally posted by Pekka
It's not a matter of belief. It's a matter of mathematial facts. DO we have a single math student here or student who has taken more than one course of math that actually disagrees with this statement?

Yes. I find it to be aesthetically false.

[Pekka]

well that certainly is true.

[KrazyHorse]

Originally posted by Dracon II
Its an asymptote, no? It comes infinitely close, but never reaches... like Zeno's paradox.

What the **** are you talking about? .9999.... doesn't move. It has a single, well defined value. That value is one.

Anybody who disputes this is henceforward declared to be an idiot.

[Pekka]

What has been shown here is few easy examples of .99999 being 1.

For example that algebra what VJ showed.

The point of it is, if you basically.. you go for an infinite loop, waiting for that .0000000001 or what ever to appear, well it's an infinet loop, it won't appear. And so the difference between the two is none, there is no difference, so they must represent the same number.

[KrazyHorse]

Originally posted by Eli
I find this question to be very disturbing.

As nice as all the proofs on wikipedia are, a number cannot equal another number when they do not have exactly the same digits everywhere.

Why? The decimal representation of a number is not the number itself

In fact, any number with a terminating decimal representation has two equivalent decimal representations, i.e. 0.382 and 0.38199999....

This is a well-known "feature" of the current decimal system.

[Pekka]

"As nice as all the proofs on wikipedia are, a number cannot equal another number when they do not have exactly the same digits everywhere."

Right. And 0.999999 and 1 represent the same number so there's no contradiction to what you just said .

What I find disturbing is the part "as nice as proofs are.." Yes. They are disturbing. Facts make my thinking box have all that static

[KrazyHorse]

Originally posted by civman2000

Spoiler:

Obviously, you need at least 3. But (0,0), (1,1), and (a,a) work where a is any transcendental.

Oh, and I'd like to challenge you in real analysis .

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)

[SlowwHand]

Originally posted by Provost Harrison
You know, this would be quite a pleasant mathematics thread, if it wasn't for the fact that some of the posters here are so f**king arrogant...

KH, right? I know what you mean. He could bottle and sell it as a scent that drives people away.

[Pekka]

KH is an angry teacher. He will kick all of our asses if we don't get stuff I guess they had to remove that poster of Machiavelli from the teacher's lounge, who put it there, confess KH!

[Lul Thyme]

Originally posted by civman2000

Spoiler:

No, the solution with 3 points works for all dimensions. Though obviously only 2 works in 1 dimension.

He he
didnt actually check.
Another victim to the Law of Small Numbers