1 = .9999.....

[NeoCracker]

Mathmatically you are getting to the nity grity technicalities. If it is getting infinately closer, you would be able to list an infinite number of numbers between the two, yet it is impossible to find but one.

And no, the is no miniscule difference in the answer, there is no difference.

Edit: That part I deleated meant absolutely nothing close to what I had intended, so for those who read it, my bad.

[oddler]

EDITGA²: Being able to argue in this thread first requires a firm background in Calculus and what 0.999... ACTUALLY MEANS. If you don't have this, you're doing it wrong and should probably just stop trying now.

Peace! See you guys later. :strut:

[NeoTifa]

Everybody just shut up and dance!

[Darkswordofchaos]

i wish i was still in school so i could ask my calculus teacher she would no

edit: you cant use a number that goes on for ever so for practicalitys sake you would have to eventualy stop it and that number would be diffrent than one but i suppose .999... would = 1 however i refuse to belive they are the same number

[Raistlin]

No, your calculus teacher would, if she knew what she was talking about, say yes. The proof is based on calculus, in fact.

.999... is not the same number as 1 if you use the two in application the diffrence in the answers youd get would be so miniscule you wouldent even be able to see it so you would apear to have the same answer. but there is a space between 1 and .999.. its just infinitly small. so in a practical and mathmatical sense they are the same number but if you wanna get down to the nity gritty technicaly no they are not the same number

That makes absolutely no sense. Between any two distinct, real numbers there exists an infinite number of other, distinct real numbers. 0.999... is clearly a real number because it is a rational number, and since you're claiming that it is distinct from 1 there should be an infinite number of other numbers between them. How about you list some?

[Tavrobel]

i wish i was still in school so i could ask my calculus teacher she would no

edit: you cant use a number that goes on for ever so for practicalitys sake you would have to eventualy stop it and that number would be diffrent than one but i suppose .999... would = 1 however i refuse to belive they are the same number

Your Calculus teacher would say yes, actually, if she were qualified to teach it. Whether or not you can use a number that is infinitely long is not the discussion here. It's about if .9... == 1, which it does. I suppose that you are willing to accept that 2/4 == 4/8 == 16/32 == 1/2, but they don't look the same, either. What's wrong with this one? There are several proofs to the situation already mentioned. It's no logical quandary.

EDIT: Man, Raist, don't ninja me.

[Darkswordofchaos]

i retract all previous statments upon studying this i have come to the conclusion that .999..... is the same as 1 my confusion comes from the fact that most mathmaticians wouldent put 1 in the place of .9999..... the would put say .9999999999999999999999999999 and end it. please forgive my ignorance

[Raistlin]

I found the calculus proof posted in an old thread. Here it is:

lim (n->infinity) Σ(i=1->n) 9/(10^i)=lim (n->infinity) Σ(i=1->n) (9/10)(1/10^(n-1))

which sets up a property of Riemann sums, so this equation becomes:

lim (n->infinity) (9/10)(1-(1/10^n))/(1-(1/10))

As n->infinity, the denominator of 1/10^n become larger and larger, and the quotient gets closer and closer to zero, and thus lim (n->infinity) 1/10^n=0. So we have:

(9/10)(1-0)/(9/10)=1

[Rye]

This entire thread = 50 patoots.

[NeoCracker]

Welcome to math Rye.

[rubah]

quick, integrate her before she escapes our bounds!

[Aerith's Knight]

If we convert her to a Taylor polynomal, she can't run due to her infinite nature!

[Ultima Shadow]

I was using finite numbers to show that they are not the same, that there are always infinately more 9's to add.

Infinity/infinity = infinity

infinity x infinity = infinity

infinity + infinity = infinity

infinity - infinity = infinity

No matter how much you add or take away from infinity, it won't change the slightest bit.



As for regarding .999 = 1. Well, the difference is infinitely small, thus it basically don't exist. Or rather, it's not allowed to exist, since it's impossible to define. Something like that. >_>

[Rye]

Noooooo, not math!

I just finished my last math requirement of my life in my first semester of college! I can't go back now! My math skills will stay and die in the Pre-Calc era of my life, because that was the highest math I got to. xD

Now that I don't have to take math anymore, I've not gotten anything lower than an A- in any of my classes! G-G-GPA boost!

(Incidentally, I did like really simple polynomials though. And by simple, I mean the really simple ones you learn in 8 or 9th grade. They were kind of fun, though I'm not sure I'd still be able to do them. )

[Tavrobel]

Infinity/infinity = infinity

infinity - infinity = infinity

These two can't be evaluated, actually. The problem with using infinity interchangeably with large numbers is that it doesn't work. You can;'t use it like that.

There is no difference; it's not infinitely small, it's non existent.