Let's see if anyone gets this, other than Zan of course!!

Ok, can anyone prove that 9.99999 repeating infinitely equals 10? or even .999999 = 1 ?? lol

I obviously can but how can 9.9 repeat infinity? Do you mean infinitely? Idk...

My calc teacher did this trick last year.

Let x = .9999...

Then 10x = 9.999...

10x - x = 9.999... - .999... = 9

9x = 9

x = 1

Slent wrote:

My calc teacher did this trick last year.

Let x = .9999...

Then 10x = 9.999...

10x - x = 9.999... - .999... = 9

9x = 9

x = 1

umm.. pretty close lol.. but your algebra is a little messed up lol
while x=9.999..
10x should = 99.999.. lol
then 10x - x would be 90 99.999.. - 9.999..
90x = 90
divide 90 from both sides blabla
and you get x = 10

and its no trick lol Its all an infinite geometric series lol

Alt you definitly just said the same thing he did bro... His Algebra is fine.

x=.9 repeating
10x=9.9repeating
10x-x=9.9repeating-.9 repeating
9x=9
x=1

Hmmmm?

And this isnt an example of an infinite series. This is simple digit manipulation. If you wanted to prove this using infinite series and sequences it would be a little different.

The most common form of decimal expansions is to define them as sums of infinite series. Which would be something like...

(X_0)(X_1)(X_2)...= X_0+X_1(1/10)+X_2(1/10)^2+X_3(1/10)^3+...

Where X is the vairable an _ denotes the subscript and a carret (^) denotes the power it is raised to.

For .999... we can apply the Convergence theorem that deals with a geometric series.

If |r|<1 then ar+ar^2+ar^3+...=(ar/(1-r))

Since .9 repeating is a sum with the common ratio of r=1/10 you simply plug it in!

.9 repeating = 9(1/10)+9(1/10)^2+...=(9(1/10)/(1-(1/10)))=1

This was actually the first proof that actually proved this and was actually introduced in 1770 by a mathmatician named Leonhard Euler.

Hope this helped answer your question... Can I have a prize yet? And please dont make me type out the sequence to obtain it... I dont know the alt number for an epsilon...

Zanathar wrote:

Alt you definitly just said the same thing he did bro... His Algebra is fine.

x=.9 repeating
10x=9.9repeating
10x-x=9.9repeating-.9 repeating
9x=9
x=1

Hmmmm?

And this isnt an example of an infinite series. This is simple digit manipulation. If you wanted to prove this using infinite series and sequences it would be a little different.

The most common form of decimal expansions is to define them as sums of infinite series. Which would be something like...

(X_0)(X_1)(X_2)...= X_0+X_1(1/10)+X_2(1/10)^2+X_3(1/10)^3+...

Where X is the vairable an _ denotes the subscript and a carret (^) denotes the power it is raised to.

For .999... we can apply the Convergence theorem that deals with a geometric series.

If |r|<1 then ar+ar^2+ar^3+...=(ar/(1-r))

Since .9 repeating is a sum with the common ratio of r=1/10 you simply plug it in!

.9 repeating = 9(1/10)+9(1/10)^2+...=(9(1/10)/(1-(1/10)))=1

This was actually the first proof that actually proved this and was actually introduced in 1770 by a mathmatician named Leonhard Euler.

Hope this helped answer your question... Can I have a prize yet? And please dont make me type out the sequence to obtain it... I dont know the alt number for an epsilon...

actually yes it is a very basic example on how to prove a part of the series... and typing things out of a book, or copying them off the internet is pretty lazy.. and funny when you use them incorrectly lol.. but good try though broski No prize for you!

You are going to tell me my proof is wrong? Some balls ya got there broski. Take it up with the 1700's scientists no this sexy monster.

Zanathar wrote:

You are going to tell me my proof is wrong? Some balls ya got there broski. Take it up with the 1700's scientists no this sexy monster.

lmao you are sooo dumb... I never said it was wrong wow haha... all I said was you were incorrect in attempting to say what I stated was wrong but yet again, a good try by the great zan .... also earlier I said "while x = 9.999.." which i meant to put in there before but forgot

I only call it a trick because it really has no significance other than to impress.

ok zan and alt, who was the one who showed you how to do this, in the hookah lounge?

Haha hey there buddy