.999999999999...=1

...I did. WTF are you talking about?

...I did. WTF are you talking about?

5th grade mathematics?

1/3 = 0.3'
2/3 = 0.6'
3/3 = 0.9'

 

This.

You don't even need to prove .9999 equals 1 because it's common sense and everybody knows it.

Nothing in this Universe approaches a number, gets all the way there, but never equals it.

You don't even need to prove .9999 equals 1 because it's common sense and everybody knows it.

Nothing in this Universe approaches a number, gets all the way there, but never equals it.

That doesn't even make sense.

It makes 100% sense to the non-morons of the world.

It makes 100% sense to the non-morons of the world.

Quiet.  The adults are talking.

Quote from: Lord_Xenu on May 29, 2011, 01:03:41 PM

It makes 100% sense to the non-morons of the world.

Quiet.  The adults are talking.

There are no adults here, just kids taking a break from Call of Duty or whacking off to porn.

Quote from: Roundy the Truthinessist on May 29, 2011, 01:06:08 PM

Quote from: Lord_Xenu on May 29, 2011, 01:03:41 PM

It makes 100% sense to the non-morons of the world.

Quiet.  The adults are talking.

There are no adults here, just kids taking a break from Call of Duty or whacking off to porn.

Actually, I'm doing both right now.

who cares about pointless idiot stupid stuff like this? seriously?? 

does anyone seriously take issue with the fact that .9 repeating = 1?

does anyone seriously take issue with the fact that .9 repeating = 1?

There are many nontrivial philosophical objections to the (typical, set theory based) concept of real numbers.

What I do not understand is why laypersons, not working in mathematics, care about such things.

It feels very sad to me that they are missing out on the beauty of serious mathematics.

IF you accept the real numbers, how can you possible reject it? I mean, 0.999... is a straight forward geometric series, S = ar/(1-r).


But something I'd be interested in is to see a proof that is compatible or uses portions from non-standard analysis and the hyperreal numbers. I believe there is a theorem that each hyperreal number is infinitely close to one and only one real number. Anyone familiar with this want to see what you can get into?

I think if 1 = 0.999..., then if 1 ≈ 1 + α and 0.999... ≈ 0.999... + β, then it would have to be true that α = β, wouldn't it? Could a proof be worked out that way?  (≈ means "is infinitely close to" in this context, and α,β are infinitesimal)

EDIT- every thing I'm seeing indicates that in the hyperreal system 0.999... < 1 by an infinitesimal amount. 

Quote from: Chris Spaghetti on March 18, 2011, 07:45:59 AM

Before we had a concept of negative numbers it would have been impossible to demonstrate that 5-7=!0

Incorrect.

I'd like to see that.

Quote from: Parsifal on May 21, 2011, 07:52:26 PM

Quote from: Chris Spaghetti on March 18, 2011, 07:45:59 AM

Before we had a concept of negative numbers it would have been impossible to demonstrate that 5-7=!0

Incorrect.

I'd like to see that.

Add 7 to both sides of the equation.

It makes 100% sense to the non-morons of the world.

You reek of logical fallacies.

an infinitesimal amount.

In the set of real numbers, "an infinitesimal amount" = 0

Quote from: ItRestsOnInfiniteTurtles on June 18, 2011, 02:09:11 PM

an infinitesimal amount.

In the set of real numbers, "an infinitesimal amount" = 0

0 is not infinitesimal, it's easy to prove that the real number system contains no infinitesimals. It's a bit harder to construct number systems which do.

I am unaware of the existence of quotation marks.

k bro

Quote from: PizzaPlanet on June 24, 2011, 12:09:47 AM

Quote from: three-dimensional-world on June 23, 2011, 03:56:00 PM

I am unaware of the existence of quotation marks.

k bro

In case you didn't know, infinitesimal has a mathematical meaning..

Yes. Your point?

0 is not infinitesimal

False.

Quote from: three-dimensional-world on June 23, 2011, 03:56:00 PM

0 is not infinitesimal

False.

What a whopper of a first post. Unfortunately, you're wrong. Something that is infinitesimal cannot be equal to zero.

ITT: 0/∞ != 0

Quote from: ItRestsOnInfiniteTurtles on June 18, 2011, 02:09:11 PM

an infinitesimal amount.

In the set of real numbers, "an infinitesimal amount" = 0

If you read my post, I was not referring to the real numbers. I was referring to the hyperreal numbers. Anyone else care to take a stab at my question in my previous post? (seems non-standard analysis is none too popluar, sadly).

Here it is again:

IF you accept the real numbers, how can you possible reject it? I mean, 0.999... is a straight forward geometric series, S = ar/(1-r).


But something I'd be interested in is to see a proof that is compatible or uses portions from non-standard analysis and the hyperreal numbers. I believe there is a theorem that each hyperreal number is infinitely close to one and only one real number. Anyone familiar with this want to see what you can get into?

I think if 1 = 0.999..., then if 1 ≈ 1 + α and 0.999... ≈ 0.999... + β, then it would have to be true that α = β, wouldn't it? Could a proof be worked out that way?  (≈ means "is infinitely close to" in this context, and α,β are infinitesimal)

EDIT- every thing I'm seeing indicates that in the hyperreal system 0.999... < 1 by an infinitesimal amount. 

It seems 0.999... is not equal to 1 in the hyperreals. I'm wondering if that is false, and if so I want to see a proof that 0.999... = 1 in the hyperreal system.

Quote from: Dr Pennyweather Macintosh on August 07, 2011, 01:49:26 AM

Quote from: three-dimensional-world on June 23, 2011, 03:56:00 PM

0 is not infinitesimal

False.

What a whopper of a first post. Unfortunately, you're wrong. Something that is infinitesimal cannot be equal to zero.

In non-standard analysis (infinitesimal calculus as described by Abraham Robinson), 0 is an infinitesimal number, if I recall correctly. Because st(x + Δx) = x, and st(x + 0) = x. Of course, I haven't looked in his free textbook for a few months, so I could be misremembering.

0,9999999999999...... <> 1

0,9999999999999...... it is NOT 1

There are infinite real numbers between 0 and 1, this lead us to the fact that for any iota ( ANY ) that allows me to consider:

x+i = 1, even if x= 0,99999999999999999.. ( you put as many 9's here as you want ), "i" is still NOT 0

You can say that 0,9999999.... is 1 in the limit ( Lim x-> 1 ; y=x ) Please, forgive this poor mathematic notation, just get the idea.

0,9999999999999...... <> 1

0,9999999999999...... it is NOT 1

There are infinite real numbers between 0 and 1, this lead us to the fact that for any iota ( ANY ) that allows me to consider:

x+i = 1, even if x= 0,99999999999999999.. ( you put as many 9's here as you want ), "i" is still NOT 0

You can say that 0,9999999.... is 1 in the limit ( Lim x-> 1 ; y=x ) Please, forgive this poor mathematic notation, just get the idea.

If you are talking about real numbers, 0.999... IS equal to 1.

0,9999999999999...... <> 1

0,9999999999999...... it is NOT 1

There are infinite real numbers between 0 and 1, this lead us to the fact that for any iota ( ANY ) that allows me to consider:

x+i = 1, even if x= 0,99999999999999999.. ( you put as many 9's here as you want ), "i" is still NOT 0

You can say that 0,9999999.... is 1 in the limit ( Lim x-> 1 ; y=x ) Please, forgive this poor mathematic notation, just get the idea.

0.(9) has infinite 9s.

There are infinite real numbers between 0 and 1, this lead us to the fact that for any iota ( ANY ) that allows me to consider:
x+i = 1, even if x= 0,99999999999999999.. ( you put as many 9's here as you want ), "i" is still NOT 0

The fact that there are infinite 9s cancels out the fact that there are infinite numbers between 0 and 1.  Would you dispute the fact that 0,333... is equal to 1/3?  If you do, I wish you luck in the third grade; if not, I hope you realize that it is the same principle at work here.  Technically you can put as many 3s after the decimal point you want, it will still not be equal to 1/3 (which by definition can't be expressed by a terminating decimal anyway); but if it's understood that there are an infinite number of 3s after the decimal point, it is equal to 1/3.

0,333... x 3 = 0,999...; do you dispute the logic?

1/3 x 3 = 1; do you dispute the math?

Therefore, 0,999... = 1.

In other words, there is no iota.

Is using commas as decimal points a convention that I am not aware of?

Is using commas as decimal points a convention that I am not aware of?

In many places (including all of Europe, I believe) it is the convention.  I'm American, of course, I just thought I'd humour him.

It's not all of Europe, but several countries do do it. That's the way I've been taught, and I had to go through a painful switching process when I moved to the UK.
Basically, those countries use a comma as a decimal point and a dot as a separator in large numbers.
0,5 would be 1/2, whereas 1.000.000 would be one million.
The reason for that is that (mostly in handwriting), it's fairly easy to not write down the dot (for example, by simply not pressing your pen hard enough), which is generally much less likely with a comma. If we miss a separator, on the other hand, it's usually no big deal (I mean, hardly anyone even uses them).