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ImCh1efPeasant

Math question! (14765 reads, 93 replies, 1 year ago)

I had a discussion with some friends (kinda nerdy discussion =d)

They thought that 9.99999999999999999999999999...=1
and I said that 9.99999999999999999999999... =/= 1

can any1 try to prove to me that I'm indeed wrong and that 9.99999999999999999999999999...=1
?

note: 9.99999999999999999999999999... means infinity amount of 9's

This post was edited by a forum moderator @ 1 year ago

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1 year ago

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37927

9.99999999999999999999999999...=1

it does not equal (nearly one), it equales nearly ten.

and no, that is not 10, it is equal the number it says, but people often cuz of lazyness write it like a whole number. Those difference is only important to people who are meticulous, and one more thing where it matters could be in atom physics or something really important, precise etc.

I like trains.

This post was edited by its author @ 1 year ago

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1 year ago

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KoyomiSandwich

#1 is right ... It's nearer to 10 ... @_@

If you're talking about 0.9999999999999.. They will never be equal

Any game can be won with the power of turtle!

This post was edited by its author @ 1 year ago

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1 year ago

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AnubiA.DemoniC

0.9999999.. will never be = 1, this goes on for an eternity however; you will always be missing that little part, which would make it 1.
I assume you mean 0.99.... and not 9.99 because then the difference is big Oo
Can't really point it out, other than in THEORY it will be different, but in the world (Atleast from what I know of) - noone can say "here, we need 0.99999999999999... gram of this in, while we need 1.00000000000... gram of this!"

TL:DR - In theory it's different, but practic use, it is not (well it is, but then again; leads back to theory)

Nerf Scissors, rocks are fine. - Paper

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1 year ago

rEd-

Nope they are nvr equal-
0.99999999.... x times < 1
9.99999999.... x times < 10 (Im assuming its one of the 2 cases i mentioned coz ur case doesn make sense..:)
In both cases 1 and 10 they are greater by exactly 0.0000.....(x-1) times1

Ps- 'x' is a variable wherein each case it refers to the number of digits after the decimal point
In the last case where i explained The calulated difference between them, '1' at the end of the result is the xth number after the decimal point(Hence zeroes upto x-1 times and then 1)
Example - If x = 5
0.99999(Five 9's)
Then 1 > o.99999 by 0.00001 (x-1 = 4 Therefore 4 zereos then 1)
Hence in ur case like u said infinite 9's where x= infinity,the differnce btwn the numbers is o.oo...(Infinity-1)1

Sry if i made it a little more complicated then it shud be..:D..i cud put it btr on paper using math terms but i dun kno how to put calculatr font here so i did what i could..Hope this answered your question

This post was edited by its author @ 1 year ago

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1 year ago

vlovo.792

its important when you talk about pricise things or about realy big amounts. like john has 0.999999 trillion dollars.

bob says, wow he has trillion dollars.

bob just miscounted by a million dollars(or something like that, i didnt actually look)

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1 year ago

anatase

Blizzard for the april fool some years ago did "prove" that 0.99999999999=1

but it was an april fool;).

In fact it won't ever be equal to 1

Holydamned sh**

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1 year ago

Jizzus

Instead of proving you wrong, ICP, don't you want a confirmation that you're actually right? :P

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1 year ago

Brewsto

Infinities are hard to understand.

Here is why your friend(s) is/are right.

x=0.999999...
10x=9.9999...
10x-x=9.999...-0.9999...
9x=9
x=1

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1 year ago

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GigaGenesis

^ your mistake is that [infinity]-[infinity] doesn't make sense so 9.999...-0.999...=/=9

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1 year ago

#10

Jizzus

2010-09-01 22:08, Brewsto wrote:
Infinities are hard to understand.

Here is why your friend(s) is/are right.

x=0.999999...
10x=9.9999...
10x-x=9.999...-0.9999...
9x=9
x=1

You owe that misconception to ignorant academics.

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1 year ago

#11

Brewsto

#10 You owe that misconception to brain failure. Quote what you think I have wrong on my previous post

#9 For you baby

This post was edited by its author @ 1 year ago

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1 year ago

#12

gt2slurp

#8 is totally right ^^

0.9999... really =1

You can't think about "the last 9", the last 9 of a periodic number does not exist. You have to think about it like limits when the number of nine tend to infinity.

x=0.999999...
10x=9.9999...
10x-x=9.999...-0.9999...
9x=9
x=1

This proof is a little straightforward but still correct. This one exist too:

1/3=0.333...
3 x 1/3 = 0.999...
1=0.999...

GtZslurp.behemoth NA server

This post was edited by its author @ 1 year ago

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1 year ago

#13

1chigo

they are in fact equal 0.9999..=1.

i guess the simplest way to explain it and understand it, is this:

9 * (1/9) = 9 * (0.111...) = 0.99999...

alternatively:

9 * (1/9) = 9/9 = 1

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1 year ago

#14

tfarcraw

nice 1! =.=

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1 year ago

#15

DoomsVille

http://lmgtfy.com/?q=does+0.9999+equal+1

Yes it is 1.

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1 year ago

#16

Jizzus

Damn, I thought I'll save myself from the trouble of typing all that... Anyway, here goes the reason why this is a misconception. I hope I can make it comprehensible enough without going into the details.

First, I have to comment on the nature of infinity why infinity and infinite "numbers" aren't actual numbers. We assume they are but reality says otherwise.

If I (infinity) + 1 = I then we could also say that I - 2 = I.

Where's the problem?

I+1=I
I-2=I

=> 1=-2

This is just another way to abuse arithmetic principles and it's only possible, because the concept of infinity came long after 1+1=2. That's why arithmetic can't account for it. Some people, questioning the possibility of having an uncertainty in maths, look for rational explanations.

I believe the explanation physics has to offer is much more beautiful, but it won't make much sense to you (or at least I don't know how to make it short and simple enough for you to understand :<).

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1 year ago

#17

Alkatraz

#16 get your facts straight

I + 1 != I

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1 year ago

#18

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Pulimuli

this is how i would say it "0.99999999...." is not equal to 1, stop being retarded"

edit: also, slap them in the face

This post was edited by its author @ 1 year ago

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1 year ago

#19

Jizzus

2010-09-01 23:06, Alkatraz wrote:
#16 get your facts straight

I + 1 != I

So, when trying to give a simple answer, I have to explain the concept of the continuum hypothesis?

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1 year ago

#20

Shaid

2010-09-01 22:53, Jizzus wrote:
Damn, I thought I'll save myself from the trouble of typing all that...

I believe the explanation physics has to offer is much more beautiful, but it won't make much sense to you (or at least I don't know how to make it short and simple enough for you to understand :<).

As a Physicist I'd love to hear this explanation.

.9999(...)=1 is a math question, not a physics, nor philosophical one as it is mathematics which defines what the equal (=) symbol means. Given the set of real numbers, the multiplication operator (*), and a uniqueness theorem we can easily show that as defined by mathematics .999(...) is in fact the same real number as 1.
For any 3 real numbers A,B, and C (excluding 0 of course) If, A*B=C*B then A=C (this holds true for any field) so given that the set of real numbers form a field under +/* and the fact that .9999999(...)*1/9 = .1111111111(...)=1*1/9
we have
.9999999(...)*1/9 = 1*1/9
.9999999(...)= 1

QED

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