Re: .999~ = 1?
 

What're you talking about? 9.99 (repeated) multiplied by 9 would have to equal 9. How would you think otherwise? Did you use something like a calculator to check it? If so... I know that you did not press enough "9"s. If you even tried... you'd fail, for you'd die.

The point of multiplying the infinite ".99" is to not "slice" it, no matter what tool you're using.


To further explain...

9 x .9 is exactly .9 less than 9... which is 8.1
9 x 9.99 is exactly .09 less than 9... which is 8.81

If this continued "infinitely", then .999 repeating multiplied by 9 would have to be exactly .0(repeating) less than 9. And I assume you know .0(repeating) equals zero, and that you cannot tack a number (such as 9, in this instance) to the end of an infinite.

Re: .999~ = 1?
 

can you phrase this differently for the sake of clarity. 9 x 9.99 is 89.91, which is exactly .09 less than 90. Maybe you meant to say 9 x .999 is 8.991 which is exactly less than 9?

The distinction of infinity is the difference. Your argument that there is no conceivable number between .999~ repeating and 1 is the clincher since a number cannot be tacked at the end of an infinite. Could there be a number to meet the infinitesimally receding value of the difference between .999~ and 1. Apparently not in a mathematical expression. So I'll admit I was wrong in an arithmetic sense. It's just a matter of grasping the concept of infinity (which I freely admit that I don't). But I keep thinking of a graph that infinitely approaches 1 as its limit.

Re: .999~ = 1?
 

me confused and .999 is not equivalent to 1, it cant be

Re: .999~ = 1?
 

In terms of a limit, .999~ may come infinetely close to 1, breaking down the difference in an arithmatic sense. But, the fact remains that it is still less than one, and that makes a difference when you calculate it with respects to infinity.

Re: .999~ = 1?
 

uhhhh..... zuh???

brain hurtz

Re: .999~ = 1?
 

No, its not, but the problem is that you cant prove that its not.

Re: .999~ = 1?
 

it isn't equal...similar to how a hyperboly will never hit the axis...it comes infinitely close....but its never quite there

Re: .999~ = 1?
 

That's all of your problems.

You're all thinking in terms of the foolish scientific theory... the theory that if someone aims to reach a destination, they will fail 100% of the time. Why, you ask? Because to get somewhere, you must travel half the distance... then half that distance... To get anywhere, you must infinitely travel half the distance. How does one manage to skip traveling half the distance? It's because infinite is irrelevant to real world applications. Infinite is a term.

A Hyperbola has limitations that this situation does not. A hyperbola gets infinitely close on purpose. A hyperbola that gets infinitely close to 1 does not cross .99(repeating), I guarantee it. A hyperbola not only gets infinitely close to a point, it also continues infinitely in a "parallel" direction (only parallel by appearance). Because it also continues infinitely and must infinitely get closer to the point... then there has to be space between the hyperbola and the line, no matter how small... so that it can get closer. In other words, since there is no number between .999(repeating) and 1 (as you can not put a number at the end of an infinite), then the point cannot feasably fit on the hyperbola, and therefor must also equal one.

I must emphasize once again that infinite is not a real number. It's applied a lot in mathematics, but it cannot be found on a number line.


If it cannot be understood that .99(repeated) is the same number as 1, then I will conclude any attempt of sensibility and leave it at the fact that this is merely a a gaming forum.

Re: .999~ = 1?
 

Scary. That made sense.

Hmmm. You use the whole "This is merely a gaming forum" everytime a topic gets tricksy or out of control. :p

But, after much reviewing (and the fact that for some reason what Rndm said finally clicked and made sense...) I have concluded that .999~ is equal to 1. Because, as random has already pointed out, the difference between the two is .000~. Though it is hard to except, because we have been tought since 1st grade that decimals do NOT equal to a whole number...

I believe that the concept of .999~ = 1 is so hard to understand because it is virtually impossible for the human mind to concieve "infinity". No matter how hard you try, you can't really get the perfect idea of "infinite" into your head.

Re: .999~ = 1?
 

Despite the fact that I sense fear in your tone (bwuahah), I am glad that you understood what I said. Congratulations. Comprehension feels good, doesn't it?

Re: .999~ = 1?
 

I fear infinity. :sneaky:

Indeed comprehension is good, but it is still hard to believe that .999~ actually equals 1.

Im going to use the knowledge I have obtained in this thread to try to score some bonus points in my AP Probability Class, or in my Pre-Calc class I take next semester.

Re: .999~ = 1?
 

Sweet... good plan. Hey, if you need more knowledge about the evil known as infinite, you know where you can attempt to find it.

Bwuahah...


*shudders*
I feel like a little hermit in a cave who is hiding from unnecessary knowledge and fears... With my, I hold the weapon to destroy it, but I fear its power... aaaaah!

Ignore that last paragraph if you value your and my sanity.

Re: .999~ = 1?
 

Your supposed to give us warnings like that BEFORE we read it. *shakes head*

And I'll try to get bonus points with what I know, and if that doesnt work, I'll need to come get some more to baffle my teacher with. :D

Re: .999~ = 1?
 

My math class is already hard enough...and now I'm on vacation. I don't feel like thinking about stuff like this...it seriously is making my brain hurt, not to mention that I just woke up.

Re: .999~ = 1?
 

But it's not just .9999999999..... Anything ending with .9999999999.... would equal the next number (that didn't make sense). Example:
3.99999999999....=4
9.99999999999....=10
2756.99999999....=2757