Math Is Fun Forum

Hoya

Member

Registered: 2013-10-29

Posts: 1

recurring discussion

refer from /mathisfun.com/9recurring.html

9X = 9.999... - 0.999...
or:    
9X = 9

But I saw in /mathisfun.com/numbers/infinity.html

∞ - ∞ is undefined.

I have confused.
Can you help me?

Last edited by Hoya (2013-10-29 17:11:59)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: recurring discussion

hi Hoya

Discussions on this and related topics come up every few months on the forum.  If you do a search on 0.99999 you'll find a number of them.

∞ - ∞ is undefined because ∞ is not a number, so the normal rules of arithmetic cannot be applied.

But 0.99999..... is a number and  has a clear value, so there's no reason why you shouldn't find an answer to the calculation

9.99999......  -  0.99999......   and get the answer 9.

What is the value of 0.99999.....   ?

Well,  we know that 1/3 = 0.33333.....

So why not 3  x  1/3 = 3 x 0.33333......   =  0.99999........

Some people argue that you shouldn't do things like this because an infinite number of 9s in a number means you cannot ever write it down, so it doesn't really exist.

I don't accept that because there are lots of numbers we cannot fully write down, eg.    pi   and    root2

Nobody wants to argue that those numbers don't exist.

Bob

Last edited by Bob (2013-10-29 20:16:25)

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Atheous

Member

Registered: 2013-10-30

Posts: 1

Re: recurring discussion

I saw this page as well, my introduction to this forum.

I wondered if the 9 is NOT recurring, say decimal 1 trillion 9s, is the value less than 1? It seems removing the infinity might render it non-equal, but I'm not math competent.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: recurring discussion

Hi;

Welcome to the forum. You are correct, 1 trillion or any other number of nines would not be good enough for it to be an equality.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: recurring discussion

hi Atheous

Welcome to the forum.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: recurring discussion

Hi Hoya and Atheous

Welcome to the forum!

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

gholamalih

Member

Registered: 2014-03-28

Posts: 1

Re: recurring discussion

Let x: 0.33333...
10x = 3.33333...
so 9x = 3.333... - x   ⇒ 9x = 3
then x=3 but x was 0.333...
why?

Last edited by gholamalih (2014-03-28 18:14:43)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: recurring discussion

Hi;

then x=3 but x was 0.333...

The mistake is there. x does not equal 3, x = 3 / 9 = 1 / 3

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.