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At 4/28/08 04:50 PM, CatherineElizabeth wrote:

At 4/28/08 04:37 PM, subpar wrote:

At 4/28/08 04:06 PM, CatherineElizabeth wrote: x = 0.9~
10x = 9.9~
10x - x = 9.9~ - x
9x = 9
x = 1
Therefore, 1 = 0.9~.

True, but the proof is idiotic, because you're practically using the assumption that 0.9~ = 1 to get to your answer. The only way that a number and ten times that number could possibly have a difference of 9 is if that number equals 1 to begin with. Simple algebra.

No where have I assumed that 0.9~ = 1. To your second sentence, that's why 0.9~ equals 1, duh!

Again...

You're saying that .9~ is a infinite number right? Doesn't that mean that it never ends? Therefor it can never equal one, but only be a approximation.

:At 4/28/08 04:53 PM, Tsuchinoko wrote:

Again...

You're saying that .9~ is a infinite number right? Doesn't that mean that it never ends? Therefor it can never equal one, but only be a approximation.

That's gibberish. Just because it never ends somehow makes it an approximation? Approximations are required for unknown or uncertain information. All information in the proof that I stated is known and is self-evident.

I'll challenge you with this question too. All numbers have an infinite amount of numbers between numbers; that is, we can come up with an infinite number of "slices" between the numbers 2 and 3. So if 0.9~ and 1 are truely different numbers, then there must be an infinite number of numbers, or slices, between them. Care to list at least one of those numbers?

Trying to prove or disprove this theory is completely pointless, and a waste of time in my opinion.

At 4/28/08 04:48 PM, Procrastination wrote: pi is excatly 3!

blasphamy!!!!!11!!!one!!!!!!!!!!!!!111!!
!!!

Rather than saying "giving infinity a value," it's perhaps a bit
clearer to say, "giving the concept of a limit of an infinite sequence
of numbers a value."

.9 is not 1; neither is .999, nor .9999999999. In fact if you stop the
expansion of 9s at any finite point, the fraction you have (like .9999
= 9999/10000) is never equal to 1. But each time you add a 9, the
error is less. In fact, with each 9, the error is ten times smaller.

You can show (using calculus or other methods) that with a large
enough number of 9s in the expansion, you can get arbitrarily close to
1, and here's the key:

THERE IS NO OTHER NUMBER THAT THE SEQUENCE GETS ARBITRARILY CLOSE TO.

Thus, if you are going to assign a value to .9999... (going on
forever), the only sensible value is 1.

Yes yes... copy and paste but it does the trick. ;)

THIS ISN'T FUCKING MATH CLASS!!!!!!!!!!!!

At 4/28/08 05:10 PM, camobch0 wrote: THIS ISN'T FUCKING MATH CLASS!!!!!!!!!!!!

Hey, it's not our fault you're mad at the public education system because it failed you.

Some one learned 6th grade algebra today!

At 4/28/08 04:51 PM, CatherineElizabeth wrote: No, but we would be in the same spot.

Physics says you can't occupy my point in space no matter what or else we'd be one thing.

Which means we wouldn't be having this conversation unless the US was schizophrenic

At 4/28/08 04:50 PM, CatherineElizabeth wrote: No where have I assumed that 0.9~ = 1. To your second sentence, that's why 0.9~ equals 1, duh!

You misunderstood my post. I'm saying that the second step of the proof doesn't work unless we already take into account that 0.999... equals 1. The reason is that, in step two, you state that multiplying 0.999... by 10 essentially equals 0.999 + 9, which only makes sense if 0.999 is 1.

What we really need is a proof that "x = 0.9~" is the same as "10x = 9.9~". Logically, it makes sense if you understand that the nines go on forever, but you probably shouldn't try to prove something like this using simple algebra. There are other ways to prove it, but they're all confusing and probably use notation that can't be typed on the forum.

Tell me, what number comes in between 0.999~ and 1? There isn't one, so 0.999~ equals one because two different numbers have an infinite number of numbers between.

I never argued that 0.999... does not equal 1. I was saying that I don't believe this particular "proof" adequately proves it.

I get the point, you can do stupid shit with numbers and make yourself look stupid. Good job.

Oh, please. There's no need to throw insults around in a discussion on mathematics. Besides, most people can't even figure out which step in that proof is impossible. Am I stupid for understanding the humor in my own post?

Bah humbug. Fuck this thread.

At 4/28/08 05:05 PM, bobbycat77 wrote: Trying to prove or disprove this theory is completely pointless, and a waste of time in my opinion.

This theory has easily been proved by a number of proofs requiring basic knowledge of algebra and in some a basic knowledge of calculus. It's just noobs who can't comprehend the logical conclusions of infinity or who can't add that challenge it. Every now and then, you will have a casual skeptic, but they easily see the light soon enough.

At 4/28/08 05:10 PM, camobch0 wrote: THIS ISN'T FUCKING MATH CLASS!!!!!!!!!!!!

Whereas math class teaches you math, what's shown here is just proof of our failure in representing fractions in the real world.

At 4/28/08 05:17 PM, CatherineElizabeth wrote: This theory has easily been proved by a number of proofs requiring basic knowledge of algebra and in some a basic knowledge of calculus. It's just noobs who can't comprehend the logical conclusions of infinity or who can't add that challenge it. Every now and then, you will have a casual skeptic, but they easily see the light soon enough.

look mate, using your proof it would appear that 0.999etc would = 1 but it physically cant, no matter how many 9s you have it will never equal 1, the difference between them would be infinitely small, but the difference would still be there, although it would be beyond our comprehension to say what the difference is.

So i suppose that if we were working only within our comprehension not what logic tells us:
Then yes 0.999etc = 1

So i suppose that if we were working only within our comprehension not what logic tells us:
Then yes 0.999etc = 1

So pretty much our mathematics system is flawed?

At 4/28/08 05:02 PM, CatherineElizabeth wrote: All numbers have an infinite amount of numbers between numbers; that is, we can come up with an infinite number of "slices" between the numbers 2 and 3. So if 0.9~ and 1 are truely different numbers, then there must be an infinite number of numbers, or slices, between them. Care to list at least one of those numbers?

Using that logic, one could easily conclude that 0.9~ does not equal 1. While they do not have an infinite number of "slices" in between them, they do not represent the same slice, but two consecutive slices, since the difference between 0.9~ and 1 is infinitesimally small and so is each slice.

Of course, logically, we know that this infinitesimally small difference is essentially zero, so the end result is the same. It's another bad proof, though.

At 4/28/08 05:28 PM, Tsuchinoko wrote:

So i suppose that if we were working only within our comprehension not what logic tells us:
Then yes 0.999etc = 1

So pretty much our mathematics system is flawed?

when you get to infinity it doesnt really matter now does it, because what practical application could it hold?

At 4/28/08 05:17 PM, subpar wrote:

At 4/28/08 04:50 PM, CatherineElizabeth wrote: No where have I assumed that 0.9~ = 1. To your second sentence, that's why 0.9~ equals 1, duh!

You misunderstood my post. I'm saying that the second step of the proof doesn't work unless we already take into account that 0.999... equals 1. The reason is that, in step two, you state that multiplying 0.999... by 10 essentially equals 0.999 + 9, which only makes sense if 0.999 is 1.

When you multiply something by ten, you move the decimal number one place to the right. 0.999~ when the decimal place is moved to the right once it becomes 9.999~. Seriously, that's 3rd grade multiplication.

Example: 2 x 10 = 20 0.1 x 10 = 1.0 See how the decimal place moved to the right once?

What we really need is a proof that "x = 0.9~" is the same as "10x = 9.9~".

Just like we need a proof that "x = 2" is the same as "10x = 20". Oh wait, divide both sides by 10 and move the decimal place to the left once. LOL, how easy!

:Logically, it makes sense if you understand that the nines go on forever, but you probably shouldn't try to prove something like this using simple algebra. There are other ways to prove it, but they're all confusing and probably use notation that can't be typed on the forum.

I've proved this perfectly. You just don't understand how to multiply something by 10. You = Epic Fail.

Tell me, what number comes in between 0.999~ and 1? There isn't one, so 0.999~ equals one because two different numbers have an infinite number of numbers between.

I never argued that 0.999... does not equal 1. I was saying that I don't believe this particular "proof" adequately proves it.

Well, I'm glad you understand that 0.9~ = 1, but disappointed that you do not consider this common proof true.

At 4/28/08 04:51 PM, CatherineElizabeth wrote:

At 4/28/08 04:42 PM, Fyndir wrote:

At 4/28/08 04:23 PM, CatherineElizabeth wrote: Standing infinitely next to you, buddy.

Still wouldn't make you me.

No, but we would be in the same spot.

If you're going to use vague terms like spot...then sure, we'd be in the same spot.

However, you still wouldn't be me, and 0.999~ is not the same as 1 because there is a 0.000...1 difference between them. (Here I am using ... to represent an excessively long string of numbers, I'm sure you understand.)

You can claim to have proved it, you can even try to back it up with your flawed understanding of reality, but the truth remains that they are two seperate numbers.

The basic consensus from newgrounds appears to be that you're wrong, would you like to try again?

In the logic area of mathematics there is extensive proof that one does, in fact, equal one and two equals two etc.
I might post it when I get back from uni.

At 4/28/08 05:35 PM, Fyndir wrote:

At 4/28/08 04:51 PM, CatherineElizabeth wrote:

At 4/28/08 04:42 PM, Fyndir wrote:

At 4/28/08 04:23 PM, CatherineElizabeth wrote: Standing infinitely next to you, buddy.

Still wouldn't make you me.

No, but we would be in the same spot.

If you're going to use vague terms like spot...then sure, we'd be in the same spot.

However, you still wouldn't be me, and 0.999~ is not the same as 1 because there is a 0.000...1 difference between them. (Here I am using ... to represent an excessively long string of numbers, I'm sure you understand.)

You can claim to have proved it, you can even try to back it up with your flawed understanding of reality, but the truth remains that they are two seperate numbers.

The least upper bound axiom
http://en.wikipedia.org/wiki/Least_upper _bound_axiom

Here's a set.

{.9, .99, .999, .9999. ,.99999, .......}

I'm sure you understand the rule of construction. Find me the least upper bound on this set. That is, find me the number that is greater than all the elements of this set, but is less than all the other numbers which are greater than all elements of this set.

For example, the least upper bound on {1, 2, 3, 4}, if we consider only the positive counting numbers, is 5.

But in the example above, consider all real numbers.

Go on, do it.

Hint: You're trapped.

So really, there can't be infinitesimally small difference between 0.9~ and 1.
________________________________________
____

I know this is a repost, but this rebuttals Fybdir's argument aswell.

The # in between 0.99999~ and 1 is infinity+1 If infinity goes on forever it would go between the two.

At 4/28/08 05:40 PM, CatherineElizabeth wrote: Least upper bound axiom, blah blah blah.

I'm not going to argue with that. I just wanted to make you explain it properly.

Surds are a government conspiracy.

At 4/28/08 05:42 PM, CatherineElizabeth wrote: {.9, .99, .999, .9999. ,.99999, .......}

I'm sure you understand the rule of construction. Find me the least upper bound on this set. That is, find me the number that is greater than all the elements of this set, but is less than all the other numbers which are greater than all elements of this set.

Following your instructions, .999999 would be the number you requested. No matter the size of the set, due to the nature of infinity, you can always add an extra nine to the end of whatever you've written and it will be a larger number than before, while still smaller than the infinite possibilities remaining. Unless we're not following a pattern here, in which case the next number would be x. x = (1.0 x 10^-%u221E) + .99999.

I. AM. PYTHAGORAS!....I mean SPARTACUS!

At 4/28/08 04:06 PM, CatherineElizabeth wrote: x = 0.9~

10x = 9.9~

10x - x = 9.9~ - x

9x = 9

x = 1

Therefore, 1 = 0.9~.

a/s/l lets cyber baby

Here's the proper version of solving it. Watch.

This is confusing....

At 4/28/08 05:35 PM, Fyndir wrote: If you're going to use vague terms like spot...then sure, we'd be in the same spot.

However, you still wouldn't be me

Numbers are a quantity, not a quality. The 'location' of the number is all there is to it. We attribute to the quantity a symbol. If we were arguing that the symbols are different, I'd think that's fairly obvious. .9~ is not the same symbol as 1. They are however, the same number.