.9 repeating is not equal to 1
some say it is..
...
Here is THEIR arguement.

http://www.youtube.com/watch?v=OeUSEZqj4wI

...
TO disprove it.

when you multiply .9# by 10.... you move one nine up to the ones place.
kinda lik this

.999#
9.99#

so when you do the subtractions you are always a nine behind...

0.99999
-9.99990
_______

see what I mean?

even though it does go on forever... the .9# mulitplied by 10 is always one nine behind FOREVER

0.9999999999999999999999999999999999999999999999999999999999
-9.9999999999999999999999999999999999999999999999999999999990
_______


FOREVER...

let me ask you?
what is .9 equal to?
what is .999 equal to?
what is .999999999 equal to?
what is .9999999999999999999999999999 equal to?
what is .99999999999999999999999999999999 equal to?
what is .9999999999
9999999999
9999999999
9999999999
9999999999
9999999999
9999999999
9999999999
9999999999
9999999999
9999999999
9999999999
9999999999
9999999999
9999999999
9999999999 equal to?

we can add on nines forever, and it would not be equal to one.

.9# is trying to express all the nines you can put on the right side of the decimal ( which is unlimited) at a single time.

That's illogical you can't represent all the possibilities in one instant.



When two atoms collide (or sub atomic particles if you want to get down and dirty) the universe doesn't whip out calculator and do an equation to see what the result is for the angle and speed each atom will have.


The universe is DIGITAL not Analog.


Kinda like this: (kinda... this really support)
atom A combines with 3 B atoms
you have 10 B atoms and 3 A atoms...

what happens to the last atom???
It doesn't do some .3# bull-crap... because it is a whole one peice...

Think about it.

and yes pi is screwy too... but I have to go.. I'll explain it later.

a particles position is a whole number
1
2
3
4
5
6
etc...

not anywhere inbetween
not 6.6
not 1.43434
not 342.43241

You'll see... I'm right

I never thought you were wrong.

Instead of writing all of that though you could have written this.

9.9999 is not equal to 10 because 9.9999 is not 10.
:P

Seriously speaking though 9.9 repeating is a decimal and 10 is a whole number.
However close they may be they are not the same thing.

Here's why 0.9# = 1:

x=0.9#
10x=9.9#
10x-x=9.9#-0.9#

9.9#-0.9#=9

10x-x=9x

9x=9
x=1

0.9#=1

o.o Wow, out of curiosity, why are you guys trying to say the same thing harder?

There's a problem with your equation drizzt7.

And that is...?

um, how did this all start anyway?

When you subtracted x from one side you don't subtract 0.9 from the other.

EDIT: Also I think you need to use division, not subtraction.

I use subtraction on purpose (division doesn't make sense...) and I did subtract 0.9#...

I know you did, you're not supposed to.

Also, correct me if I'm wrong, 10x is multiplication (10 times x) so you use the inverse, which is division.

Here's it simply said, and will end all need for this topic.
9.9999... is very close to 10. However, there is that infinite .1111111111... difference. End of story.

QuoteWhen you subtracted x from one side you don't subtract 0.9 from the other.

EDIT: Also I think you need to use division, not subtraction.
Nope, his equation was right. x equals 0.9# in the first place, so upon subtracting x from both sides he can use the substitution property to replace the x on the right side with 0.9#. They are, after all, equal.

QuoteAlso, correct me if I'm wrong, 10x is multiplication (10 times x) so you use the inverse, which is division.
That's when isolating the variable...but either way, you always have to do to one side what you do to the other. So he can subtract from the left side as long as he subtracts an equal amount from the right side, and since as I mentioned in this case x=0.9# is a given, what he did is valid. =)

QuoteHere's it simply said, and will end all need for this topic.
9.9999... is very close to 10. However, there is that infinite .1111111111... difference. End of story.
Then explain drizzt's equation...;)

No, there is not that infinite .1# because .9#+.1# is not 1. It is about .1 over 1.

The equation I gave you is correct and works.

To test if a number is equal to a number, you must check to see if there is a number you can add to that number to make it equal. There is no number you can add to .9# because you can't add that infinity-ith place + 1 because infinity is infinity.

Basically you would need to find if there is a finite end to the .99999 etc.

If you find it, let's say it's 0.9999999 then you would need to add 0.0000001.

Also, thanks Soul, I stand corrected.

Thats the point. Because it is infinite, it is equal to 1. If it was finite, it would not be. There is no number you can add to .9 repeating without making it greater than 1, therefore it is equal to 1.

You could add zero!
But that would be useless. But, drizzt7 is correct IMO. It seems more logical to me and makes more sense.
It would only work with finite ends. Plus, how can we tell if it is a Universal Law?

Its universal law because under no circumstances can it be proven false ^_^
Official way of puttin it.

Yes but I can prove one thing.
You didn't really make 0.9 = 1

You just eliminated 0.9 from the equation.

It's a math trick.

No, it works mathematically. My teacher said it works, my dad (masters in math) said it works, and he said all professors he's had said it works.

As long as I follow all mathematical rules and it works, it is true and you can't deny it. Whether I take it out of the equation or not, it still mathematically is sound.

I'm not denying it.
It is solid.
No doubt.

I'm just saying how it works.

QuoteIts universal law because under no circumstances can it be proven false ^_^
Official way of puttin it.

Ah, but if that's just a theory. Unless if we're omniscient, we can't truely know.

My logic:

I don't even think .99999999999 exists by some terms. The reason? What two numbers do you divide to get it? No two work. If you take the smallest possible piece off of something, THEN you get .999999 etc. But this is infinitely small. From MY standpoint, if you say .99. . . = 1 then you are saying you can get the same thing by taking away a greater-than-0 value from a number. Impossible.

QuoteBasically you would need to find if there is a finite end to the .99999 etc.

If you find it, let's say it's 0.9999999 then you would need to add 0.0000001.

Also, thanks Soul, I stand corrected.
^_^

I love math puzzles/paradoxes like this.

Weren't people a long time ago saying that 2+2=5?

Heh, this is an interesting topic.
I'm gonna take the side 0f 0.9#=1.
There are infinite 9s. Saying a 0 will be created is like saying that there is an infinity+1.
Take 1/3 (0.3#) for example.
1/3 x 10 = 3 and 1/3
3 and 1/3 = 3.3#. There's no 0 at the end.
QuoteIt's a math trick.No such thing, there is no sleight-of -hand involved in math. What people forget is that it's just numbers, I'd like to see someone counting cows and mysteriously make one disappear. :D
QuoteWeren't people a long time ago saying that 2+2=5?Ultimately, that was barely math related at all (). It was more an exploration into open-mindedness and defining 'truth'.

Quote
However, there is that infinite .1111111111... difference

Sorry to be a little stingy, but it's a .000000... ...0001 difference. .9# + .1# would sum up to 1.1#, where the last digit is a zero (that means that you ignore it though, but it has one less digit than infinity (but infinity - 1 is still not a 'real' number (in the fashion that it can't be expressed with digits and calculation signs only) it doesn't really matter))

...um, anyway, I think that 0.9# is not equal to 1, but since when does you need to use infinite decimals for calculation? Anyway, the difference is so extemely small that it can just be ignored, like when you get 33.3 cent off when there's a 30% off sale and you buy something for one dollar.

Actually, the difference should be 0, since infinity * 0 is the only equation where infinity is multiplicated with something and turns out to a... concrete number. infinity * 0.5 is equal to infinity too, and 1/infinity turns out to 0 in practice, since you can keep chopping and chopping forever. But yet, in theory there are still a little little unit... (oh, I'm getting a headache...)