Is 1 = 0.9999......

[Kyteland]

Originally posted by: bleeb
BUT, I'm still holding on to the belief that 0.9999... != 1. (Until the 1000th post)

So does the 1000th poster get to decide the final outcome of the debate?

 

[bleeb]

Originally posted by: Kyteland

Originally posted by: bleeb
BUT, I'm still holding on to the belief that 0.9999... != 1. (Until the 1000th post)

Man, I already "paraphrased" your previous post to prove that you actually think 0.99...=1, regardless of anything else you say. My logic is immuatble. Give it up already

Why are you trying to stop the fun i'm having?

 

[bleeb]

Originally posted by: Kyteland

Originally posted by: bleeb
BUT, I'm still holding on to the belief that 0.9999... != 1. (Until the 1000th post)

So does the 1000th poster get to decide the final outcome of the debate?

well i'll finally and offically say what I believe regarding this topic.

 

[Kyteland]

Originally posted by: bleeb

Originally posted by: Kyteland

Originally posted by: bleeb
BUT, I'm still holding on to the belief that 0.9999... != 1. (Until the 1000th post)

Man, I already "paraphrased" your previous post to prove that you actually think 0.99...=1, regardless of anything else you say. My logic is immuatble. Give it up already

Why are you trying to stop the fun i'm having?

Just trying to ensure that there is no 1000th post.

I seem to be failing in those regards....

 

[bleeb]

Originally posted by: Kyteland

Originally posted by: bleeb

Originally posted by: Kyteland

Originally posted by: bleeb
BUT, I'm still holding on to the belief that 0.9999... != 1. (Until the 1000th post)

Man, I already "paraphrased" your previous post to prove that you actually think 0.99...=1, regardless of anything else you say. My logic is immuatble. Give it up already

Why are you trying to stop the fun i'm having?

Just trying to ensure that there is no 1000th post.

I seem to be failing in those regards....

C'mon, lets try to get this sucker to get over 1000 posts!

EDIT: Its already past 800 posts!! i'm amazed it has gone this far...lets keep the partying going man!

 

[Kyteland]

Originally posted by: bleeb

C'mon, lets try to get this sucker to get over 1000 posts!

How about this? You and I can alternate posting.

You: IS NOT!!

Me: IS TOO!!!!!

You: IS NOTTT!!!!!!!!!11

Me: IS TOO!!! IS TOO!!!!!!!!!0.99.......

And we can se if we get to 1000 posts before we get banned.

 

[bleeb]

Originally posted by: Kyteland

Originally posted by: bleeb

C'mon, lets try to get this sucker to get over 1000 posts!

How about this? You and I can alternate posting.

You: IS NOT!!

Me: IS TOO!!!!!

You: IS NOTTT!!!!!!!!!11

Me: IS TOO!!! IS TOO!!!!!!!!!0.99.......

And we can se if we get to 1000 posts before we get banned.

Yeah we should stop posting pretty soon so we don't reach the threshold of the Banning Moderator.

 

[silverpig]

Originally posted by: JupiterJones

Originally posted by: silverpig

Originally posted by: bleeb
HOW is it possible to have different sized of infinity???? please explain.

0.9999.... != 1

There are actually different sizes of infinity, called cardinality. Aleph-null is the first size of infinity, corresponding to the number of integers. Aleph-one is the next level. I'll try and come up with an explanation if I can find it somewhere here...

I've read about this mumbo jumbo being put out by set theorist, but it won't last. Infinity = Infinity. 2 X Infinity = Infinity. Cardinality of the set of even positive integers = Infinity. Cardinality of the set of positive integers = Infinity. Infinity = Infinity.

Karl Friedrich Gauss noted that while one can think of an object like the natural numbers always reaching towards infinite size, thinking about infinity as something that has been reached, as if it were existing in a finished form was contrary to the principles of mathematics. THIS is the error of the set theorist.

Did you read my post with the cards?

 

[MadRat]

Originally posted by: DrPizza
OMG, I run into innumeracy while teaching all the time! Now, while I take a brief rest from fighting innumeracy in the high school, I find that this thread is filled with innumerates (and fortunately with many of you who do have some math skills.)

Since it isn't a democracy, the vote at the beginning of this thread doesn't matter.

.9999999 repeating equals exactly 1.0000000000000 no more, no less. If you disagree, you're a moron. It's been proven plenty of times. It can be proven in several different mathematically sound ways. Accept it.

But, wanting to add to the headaches of those innumerates among you, let me toss out this for you to ponder.

There are as many positive even integers as there are positive integers.
That is:
2,4,6,8,10,...... has an infinite number of elements.
1,2,3,4,5,6..... also has an infinite number of elements.
And, both of these infinities are the same size. There aren't twice as many integers as there are even integers. For every integer, there is a corresponding even integer. (multiply that integer by 2). For every even integer, there is a corresponding integer (divide that integer by 2). So, there is an even pairing between the two sets of elements.

Now, for the fun part. While *those* two infinities are the same size, there ARE different sizes of infinity.
Ponder that for a bit... get an interesting math book to read... and take 2 or 3 tylenol for the headache.

I see you're having fun with the definition of infinity.

Fortunately we are concentrating on the reason why one cannot compare 9's in the .999... to finite values and the reasoning is much simpler than your play on the definition.

 

[Haircut]

Madrat, what exactly is wrong with what DrPizza posted?
Please provide some actual answers instead of just telling people that they are wrong.

Also, we can compare the 9s in 0.999... to the integers.

Since 0.999... = 9 * Sum [n=1..infinity] 0.1^n.
n is an integer, so we have the 1st 9, 2nd 9 etc. i.e the 9s have a 1 to 1 correspondence with the integers

 

[DrPizza]

Yes, I know I made it more complicated than it needed to be.... just having fun with it.
I picked cardinality from the set of things that give me headaches thinking about. (and I do like the example with the cards... it seems to work better as a first example than the cardinality of numbers between 0 and 1. - not that it's not a good example... it's just harder to illustrate)

 

[DrPizza]

Like a fool, I subscribed to this thread.... so, while you guys are trying to get 1000 posts.... I think I'll unsubscribe to avoid the 1000 emails!

 

[pyonir]

1 does in fact = .999999

 

[RossGr]

The night crew, checking in for a passdown, Good job Sliverpig and Haircut its good to know that the day shift is here represting Trhuth, Justice and the American way.

Bleep, You may notice that I generally do not respond to you posts, simply because you have admitted over and over again that you are simply keeping the tread alive! I have no idea what you really think about the issue.

Other breaking news, at 8:00am PST Sunday 9Feb, I board a jet plane bound for 2 weeks in the wilds of the frozen NE. I'll be in Allentown Pa with no regular internet or even computer access! Akk!!! How am I going to survive! So if we are going to hit 1000 before I leave we need to get to work.

This whole OT discussion of Cardinality should count as a penelty, and not be counted toward the 1000, Lets stick to the topic.

But just to through my $.02 , Since the digits of every real number can be placed into a 1 to 1 correspondence with the Integers (That meaning counting, for kindergardener still learning the concept, (ie Matrat)) every individual real number cantains at mose a countable infinity of digits. This make the set of Real numbers a power set of the integers, this means that the set of Reals is NOT countable which means you cannot assign a integer to each real number, no mattter how you count them you will always miss some.
Gads its late! I have some stuff to scan and post before I head out to work.

 

[RossGr]

Here is a scan of a few pages from Principles of Mathematical Analysis By Walter Rudin

It is a short developement of the Real numbers with the extension to include infinity, The symbol Q=> Rational
numbers.

Fortunately we are concentrating on the reason why one cannot compare 9's in the .999... to finite values and the reasoning is much simpler than your play on the definition.

If I cannot compare .999... to finite values that must mean it is infinite, When and how does this number get past 1?

Or let us consider the series of numbers

.9
.99
.999
.
.
.999...(100 million 9s)

Is is safe to say that all of these numbers are less then 1?

how many nines does it take to get past 1? If I put 200 million million 9s would we get past 1?

Wait a minute has ANY ONE ever written out the integers to 200 Million Million? does that integer exist because no one has written it down?

This requirement of haveing to be able to write something down is ludricious and can have no meaning in the world of math.

Madrat,
I will note that you did not answer a single one of my questions. Why?

 

[MadRat]

You still haven't apologized.

 

[MadRat]

Originally posted by: Haircut
Madrat, what exactly is wrong with what DrPizza posted?

I don't think anything in my post said he was wrong. If anything he has a good grasp on infinity.

 

[RossGr]

Originally posted by: MadRat
You still haven't apologized.

Apologized for what?

 

[bleeb]

Originally posted by: RossGr

Originally posted by: MadRat
You still haven't apologized.

Apologized for what?

?

 

[silverpig]

MadRat thinks Ross is attacking him personally instead of attacking his ignorance.

 

[bleeb]

oh okay... so back to cardinality... subsets and spaces... Ouch. The pain comes back to me from my Combinatorics classes.

 

[RossGr]

Originally posted by: silverpig
MadRat thinks Ross is attacking him personally instead of attacking his ignorance.

Since he can't address the topic he needs an excuse to avoid answering questions. As far a personal attacks go, I have ignored repeated assults of his, I thought that was life on the web.

 

[MadRat]

If you live on the web then go ahead and live by those standards.

 

[RossGr]

Forgive is forget is basic in life, ... for most of us.

 

[AbsolutZero]

Bad thread. Bad. Play dead. Good dog.