.9999999 = 1

[BroTrevor]

Ok, this was a worthy read. I figure JMG will be all over this one.

.9999 = 1 (http://polymathematics.typepad.com/polymath/2006/06/no_im_sorry_it_.html)

Also, check out the "mr. W... I am your father" link on the side....that was a pretty funny read if you ask me.

[joris]

now, that substraction at first, it's rubbish; if I have

3x = 3
- x = 2
-----------
2x = 1

proving 1 = 2 or 2 = 1, or both; now, see, that doesn't have much to do with math

Then... 1/3 = 0.333...
that repetition, it's a kludge; that's worthless to do math with, and it just shows that some fractions cannot be written out with decimal-point notation
yes, pi is one of those that cannot be written out, only approximated; that's not nice, but it's just how it is

anyway ;) who came up with that 0.9...

[JoeC]

So, if .9 repeating = 1 because there is no number between the two,. by that same token .8 repeating must = .9 repeating which equals 1.

So, taking that a little further, .1 repeating must equal 1. Taken further, 0 = 1.

Rubish I say!

[Jezz]

Actually:
10x = 9.999...
x = 0.9999... (BUT it has one extra nine because the decimal point has moved)
10x-x = 9.999.. - 0.9999... = 8.999....1
-------------
9x = 8.999...1

Satan would love us all to believe that 0.999 = 1 because if that were true then being just one word off would still be 100% the truth.

"Hogwash! You must be a public school teacher." - I found that comment funny

[JoeC]

So, if .9 repeating = 1 because there is no number between the two,. by that same token .8 repeating must = .9 repeating which equals 1.

So, taking that a little further, .1 repeating must equal 1. Taken further, 0 = 1.

Rubish I say!

I stand corrected. There is a number between .8 repeating. Actually, a lot of them. 9.0, for example. By definition, .9 repeating does indeed equal 1, since there are no real numbers between .9 repeating and 1.

[NoahL]

So I hate to go off topic already... but is this really a thread that needs to be in the Fort? Seems like this doesn't have to be a guys only subject....

[BroTrevor]

So I hate to go off topic already... but is this really a thread that needs to be in the Fort? Seems like this doesn't have to be a guys only subject....

Most of the girls are quite uninterested in Mathmatics. It's a left brain thing.

[NoahL]

Do you mean they 'left' their brain at home? :P

[Jezz]

Hahahaha!!!

[Christian-Samurai]

So I hate to go off topic already... but is this really a thread that needs to be in the Fort? Seems like this doesn't have to be a guys only subject....
are you saying you want to share with the girls? there is plenty of other posting spots to do that, the "guys" are just having some fun with something they enjoy just cause your board with the topic doesnt mean we need to bring the girls into it :P lol

[BroTrevor]

are you saying you want to share with the girls? there is plenty of other posting spots to do that, the "guys" are just having some fun with something they enjoy just cause your board with the topic doesnt mean we need to bring the girls into it :P lol

Well spoken sir!

[JMG]

So, if .9 repeating = 1 because there is no number between the two,. by that same token .8 repeating must = .9 repeating which equals 1.

So, taking that a little further, .1 repeating must equal 1. Taken further, 0 = 1.

Rubish I say!


NO no no... Josiah your deduction is absurd!

Defining "..." as a sign of repetition .9999... = 1.
However .999 ( take note, no "...", therefore it is not a repeating number ) does not equal 1!

.89999... = .9
But .8999 does not equal .9 !

.7999... = .8
But .7999 does not equal .8 !

Also, .8888... does not equal .9 !


To remedy the situation grasp the concept by looking at the whole picture through covergent infinite series.

The reason .999999... equals 1 is that it converges to 1.
The reason .8999999... equals .9 is that it converges to .9.
.111111... = .1 because it converges to .1.
Unfortunately I cannot post equations or graphs on the forums, for if I could post equations and graphs here I would show the infinite series and graphs confirming that .99999... converges to 1, .89999... converges to .9, .11111 converges to .1, and etc.

[JMG]

Also, .8888... coverges to .89.
But .8888... does not converge to .89..., it only congverges to .89.

[JMG]

Excus me, .111111... does not converge to .1, .11111... converges to .11111...

[JoeC]

NO no no... Josiah your deduction is absurd!

Joseph, that really was not called for. Not when I had already corrected my mistake.

[JMG]

Ah, you are right, you did already remedy the situation! :y10:
I apologize Josiah. Do you forgive me?

[joris]

Excus me, .111111... does not converge to .1, .11111... converges to .11111...

.11111... is equal to 1/9; it sure doesn't converge to 1/10
if it did, we had some serious problem ;)

[JoeC]

Ah, you are right, you did already remedy the situation! :y10:
I apologize Josiah. Do you forgive me?

Of course I forgive you. :)

[JMG]

......... :)