Mathematics to reconsider

[+Colibri]

I heard there's been a long discussion on a WoW forum about this. Let's see how it goes here.

I believe there's a definite answer to the question, but i wont reveal it yet.

[Cope]

Purely technically speaking:

0.99999 = 1.0 - .00001

But, practically speaking, they are equal. Since you didn't post the poll in the scope of practicality I have to assume it was a question of technicality, so my answer is "no, they are not equal"

[strider]

This is an old argument between computer scientists and mathmaticians.

Better illustrated with the following question having two valid answers one in each of the schools.

How many numbers are there between 0 and 1.

The Mathematician's answer is: an infinate number.

The Computer Scientist's answer is: 2 to the n-1 where n is the number of bits available to represent the number.

This reminds me of the old college joke.

A maried mathematician and a computer scientist are placed in the middle of a football field and thier spouses placed at each goal line.

The referee tells them that at each whisle signal they can move half
way toward thier respective spouses.

The ref blows his whistle and the computer scientist
starts running down the field.

The mathematian says "Where do you think your going, you know you can't ever reach the goal!"

The Computer Scientist answers him, "Yes, but I'll get close enough for all pratical purposes!"

[Lindon]

i'll vote no since it needs to be whole.

[OtisTheMuffin]

No. Plain and simply no.

[Cree A'dor]

My calculator will round up if I keep plugging in nines. Of course, I don't always ask my calculator to solve all of my life's problems, just the ones it comprehends.

I vote Yes. I believe that 1.0 and 0.99999 are equal. I'm not going to bore anyone with the use of significant figures or anything, but I don't see why they have to differ really.

It all depends on what you're looking at. I like to consider the option of "units". If it's 99.999% guaranteed to kill all germs, they mean to tell you, "It's 100% guaranteed to kill all known germs to date, but in the care a new germ should ever be introduced; we are not 100% sure it will kill it, but there is a good chance. "

And if you're talking about chemicals, then they differ dramatically. You could say, "Well, the <insert fancy science noun> will be stable at or below 0.99999 µgPb but with 1.0 it could blow up!" Then no, they are not equal.

For the sake of argument, I will go with my gut instinct and just say Yes. (I never listened in school, I always said, "Yes.")

[KnitePrince]

"Backs out of the thread slowly so as not to be noticed.. and runs"

[Controlled Chaos]

It seems like everyone so far has failed to notice the elipses that follow the 0.99999, which means the number +Coli is trying to relate to us is a repeating decimal. So, is 0.999999999999999999999999(you get the idea) equal to the whole number 1?

No.

Simply because the number continues on with a string of nines into infinity, that doesn't make it equal to a whole number. The only thing that we need to be looking at here is the number before the decimal, 0. Strangely enough, zero does not equal one... nor do any of the numbers between zero and one equal one.

Simply speaking, only one can be equal to one. Anything less than or greater than one are, respectively, greater than or less than one. In this case, the number is less than one.

Another point to be made here... one is an integer, whereas 0.9999999~ is not. Any decimal/fraction between integers are not equal to those ingegers.

Just my two cents.

[+Colibri]

Good good

Well i'm a "computer scientist" so for practical purposes they are the same. But in reality, they aren't.

[Bubba Ho Tep]

No matter how much you try do make a difference between 1 and 0,99999999999999999999999999999999999999999, it will always be a 9 to the left closer than that.

[rsherman]

I'll add to this

Does 0.2 = 1 - (4/5) ?

[+Colibri]

I believe so, where's the catch?

[Gumbi]

proof that .99999... = 1 aka 9.9999... =10
a = 9.999999...
10a = 99.999999...
10a - a = 90
9a = 90
a = 10

[Kaervas]

proof that .99999... = 1 aka 9.9999... =10
a = 9.999999...
10a = 99.999999...
10a - a = 90
9a = 90
a = 10

It doesn't really work like that though. That's a flaw of representing recurring numbers in normal day to day typing.

10a would be, in it's "truest" components:

• 9.9999999999999999999999999999999999999...
  9.9999999999999999999999999999999999999...
  9.9999999999999999999999999999999999999...
  9.9999999999999999999999999999999999999...
  9.9999999999999999999999999999999999999...
  9.9999999999999999999999999999999999999...
  9.9999999999999999999999999999999999999...
  9.9999999999999999999999999999999999999...
  9.9999999999999999999999999999999999999...
  9.9999999999999999999999999999999999999...

By saying that "10a" is 99.999999999999999999999999, and that "10a - a" is 90, you are smoothing over the fact that what exactly is left when you take 1a from 10a, "9a" is not actually 90.
It is the sum of:

• 9.9999999999999999999999999999999999999...
  9.9999999999999999999999999999999999999...
  9.9999999999999999999999999999999999999...
  9.9999999999999999999999999999999999999...
  9.9999999999999999999999999999999999999...
  9.9999999999999999999999999999999999999...
  9.9999999999999999999999999999999999999...
  9.9999999999999999999999999999999999999...
  9.9999999999999999999999999999999999999...

So it is very slightly under 90.

[+Colibri]

Hmm, maybe you can use directly 0.999 for a.

a = 0.9999999....
10a = 9.999999...

10a - a = 9.999... - 0.9999...
9a = 9
a = 1


Hmm did i just proove myself wrong?

It is actually true. Because if you substract 0.9999999... from 9.999999...., you basically get 9. No matter how many numbers you write in there. That's how they taught us in school.