Curse

TopGun · Jan 30, 2006, 10:58 PM // 22:58

.999... = 1?

For those of you that DO think .999... = 1, tell me, what does .888... equal? What about .889... equal? Better yet, what about .998...? Does .998... = .999...? Or does .998 = 1?

Now, I'm not completely denouncing the capability of .999... to equal 1, but it does really make me wonder, you know? Because doesn't that sort of leave .999... dangling out there in space? There's like, this, miniscule gap between .998... and 1. It just makes my mind boggle.

So can someone please explain this to me? Why does .999... = 1?

Lasareth · Jan 30, 2006, 11:03 PM // 23:03

Reminds me of LUE All over again

There's probably some silly number theory to dispute this, but as an engineer, for all practical purposes, something with a differential increment such as 0.9999... -> 1 is rounded up to 1.

Don't forget that 0.99999... is in itself an approximation. There's no real way to desribe fractions that repeatedly run on in a numerical format. So, look at your problem this way: Why does 1/3 + 1/3 +1/3 = 1? It becomes fairly simple then

kdhoney44 · Jan 30, 2006, 11:05 PM // 23:05

Not to be too annoying here...but that can be arguable by how many significant digits you can carry. This applies especially if you are measuring something and rounding .9999 up to 1. For info on what significant digits are check out http://www.physics.uoguelph.ca/tutor...ig/SIG_dig.htm

Lasareth · Jan 30, 2006, 11:07 PM // 23:07

If that was in response to my post, I think it can be regarded the same

After all, if you have to carry it to 10 sig figs, you'll end up rounding it to 1.000000000, if 1 s.f. then 1. Same thing, though, you'll always round up to 1

Just with a different amount of placeholders.

This is assuming we're referring to 0.9999... as an interminable decimal. If it in fact does terminate at some point then yes, you can possibly have 0.9999... as an answer.

Shattered Self · Jan 30, 2006, 11:08 PM // 23:08

x = 0.9999999...(etc.)

10x = 9.99999999...(etc.)

10x-x = 9.999999 - 0.999999
9x = 9
x = 1
0.999999999...(etc.) = 1

Mentalmdc · Jan 30, 2006, 11:09 PM // 23:09

Its because if you go on to infinity, then you have a gap so small that by all means of counting and on every way you think about it the tiny difference between 0.9999999999... and 1 is as good as non existant.

How about this:

1/0=oo

To all the un-mathsy people

/ is the same as divide and...
oo means infinity

this will work with any number divided by zero, try it on a calculator, You shold get an error, as computers cant cope with infinity.

e.g.

12/2 is the same as saying, how many times does 2 go into 12, and of course the answer is 6,

and so...
12/0 is the same as saying, how many times does 0 go into 12. Think about it.......

-THE M-

kdhoney44 · Jan 30, 2006, 11:12 PM // 23:12

That wasnt in response to yours....I was typing it same time

But yes it is saying about the same thing

kdhoney44 · Jan 30, 2006, 11:25 PM // 23:25

Quote:

Originally Posted by Mentalmdc

Its because if you go on to infinity, then you have a gap so small that by all means of counting and on every way you think about it the tiny difference between 0.9999999999... and 1 is as good as non existant.

How about this:

1/0=oo

To all the un-mathsy people

/ is the same as divide and...
oo means infinity

this will work with any number divided by zero, try it on a calculator, You shold get an error, as computers cant cope with infinity.

Since I'm a math person I have to say that any number divided by zero does not equal infinity. It is considered to be undefined . The reason that a calculator cannot compute this is because ...

From the definiton of division: If 6/2=3 then 3*2=6.
If 6/0=x then x*0=6 <----This is what a calculator sees and starts to scream, since it is impossible to multiply any number by zero and get something other than zero.

Mentalmdc · Jan 30, 2006, 11:39 PM // 23:39

I would not call myself a mathsy person in the sense that i have qualifications etc, but i am about to get A* in my GCSE Maths

I thought about by saying (as in my above example) how many X go into Y, so how many 0 go into 1. My understanding of this was that you could continue putting 0's into 1 but as you are actually putting nothing at all into 1 you can go on forever doing it, thus the answer is infinity.

Comments, thoughts.....

P.S. i'm not saying your wrong in any way, its just a suggestion and how i thought about it,its probably likel i have a very skewed logic and am actually, totally out of my tree!!

kdhoney44 · Jan 30, 2006, 11:47 PM // 23:47

Your logic is correct but the problem is that you can't say something is equal to infinity, because infinity is not defined as a number. Again with the X*0=6 example. This shows you why it cant be infinity. If it where then that would say that there are infinitly many solutions for x. But in reality there are none and the equation is untrue. That is why it is called undefined instead.

(just as a side note...I have a master's degree in Math and have taught calculus and college algebra. That does't make me right it just means I have answered the question of infinity vs undefined way too many times..lol. Also congrats on getting an A in any math course..that is a real accomplishment

)

Maxiemonster · Jan 30, 2006, 11:50 PM // 23:50

Shattered Self is right.

PieXags · Jan 31, 2006, 12:03 AM // 00:03

In an exact sense, 0.99999999...(etc) is it's own number (or as close to being defined as a number that it will work for our purposes).

I think every one of us can acknowledge that 0.9999999...(etc) is in fact it's own number, that while insanely close to 1, is not 1. If 0.999999999...(etc) WAS equal to 1, we would never write out 0.9999999...(etc) as it would never have any purpose.

We might as well call it 1, but it's not 1. It's 0.9999999...(etc). I guess the more confusing question is who really cares?

(Obviously...those of us who've posted, I guess.)

xxSilhouette · Jan 31, 2006, 12:06 AM // 00:06

Well .999 equals 1 mainly beacuse it is easier to look at that way. Thats my opinion.

bulletsmile · Jan 31, 2006, 12:09 AM // 00:09

lol, this is like how to multiply two equal numbers to get 2??
like 1,5*1,5=2,25
1,25*1,25=1,5625
1,3*1,3=1,69
1,4*1,4=1,96
...........

...
i don't think anyone knows what the final number is yet:P, becouse it always end up with 1,462398278937987123729874983092848738473897040353 57454787386432890478369478
something like that

Lasareth · Jan 31, 2006, 12:11 AM // 00:11

Quote:

Originally Posted by bulletsmile

lol, this is likehow to multiply two equal numbers to get 2??
like 1,5*1,5=2,25
1,25*1,25=1,5625
1,3*1,3=1,69
1,4*1,4=1,96
...........

...
i don't think anyone knows what the final number is yet:P, becouse it always end up with 1,462398278937987123729874983092848738473897040353 57454787386432890478369478
something like that

That's because the square root of two is an irrational number :P there's lots of numbers like that. The square root of 3 is as well.

DeepFyre · Jan 31, 2006, 12:18 AM // 00:18

Quote:

Originally Posted by Lasareth

There's no real way to desribe fractions that repeatedly run on in a numerical format.

wrong - anynumber (other than a mutliple of 11) divided by 11 will give you an interminably repeating decimal

for an answer to this highly opinionated question:
http://mathforum.org/library/drmath/view/55746.html

darkMishkin · Jan 31, 2006, 12:20 AM // 00:20

Quote:

Originally Posted by Square root of Lasareth

That's because the square root of two is an irrational number :P there's lots of numbers like that. The square root of 3 is as well.

So's the square root of the square root of 4.

Lasareth · Jan 31, 2006, 12:29 AM // 00:29

Quote:

Originally Posted by DeepFyre

wrong - anynumber (other than a mutliple of 11) divided by 11 will give you an interminably repeating decimal

for an answer to this highly opinionated question:
http://mathforum.org/library/drmath/view/55746.html

A mistake in my wording

I meant it's impossible to depict such a character without some sort of special notation. The provided link explains it a bit more substantially. As an infinitely repeating number it's a special case and approaches a limit that it never reaches.

Quote:

Originally Posted by darkMishkin

So's the square root of the square root of 4.

o rly

TheOneAndOnlyX · Jan 31, 2006, 01:51 AM // 01:51

Quote:

Originally Posted by Lasareth

o rly

Ya rly!

I recently got this math question in my class

Paul Mahdi · Jan 31, 2006, 02:08 AM // 02:08

Quote:

Originally Posted by Mentalmdc

Its because if you go on to infinity, then you have a gap so small that by all means of counting and on every way you think about it the tiny difference between 0.9999999999... and 1 is as good as non existant.

How about this:

1/0=oo

To all the un-mathsy people

/ is the same as divide and...
oo means infinity

this will work with any number divided by zero, try it on a calculator, You shold get an error, as computers cant cope with infinity.

e.g.

12/2 is the same as saying, how many times does 2 go into 12, and of course the answer is 6,

and so...
12/0 is the same as saying, how many times does 0 go into 12. Think about it.......

-THE M-

Don't get me started on infinity
.999... equals 1 because because you round up.
That means (if you are rounding due to a problem you need to solve) that your answer will be slightly off.
Now .998... is also equal to 1 due to rounding. Once again your answer will be slightly off. Now .997... is also equal to 1 due to rounding (although many people would question rounding the number by now). Now your answer will be alittle more then slightly off. If you haven't stopped reading by now you are strange. Now .996 is only equal to 1 if you take the fact literaly that rounding centers around the magic little number i like to call 5. Uuuummmm...

To conclude alot of math is flawed when you think about it.

for example: pi.