You might actually be able to debate if you provided reasons @OP

There's no fucking debate that's not how this works.

i just don't like the idea of thinking of 0.99... as a number, since the number is 1. it's like -0. i don't like -0 as a number either. but i guess this debate was even more drawn out than the global warming one i was having. so i'd better stop talking about it now.

Infinity used in calculations can only really be defined in terms of limits. So when you say 1/infinity = ? and .9 recurring = ? what you mean is:

Limit as x->infinity of 1/x = ?
Limit as x->infinity of (sum from a = 1 to x of 9/(10^a)) = ?

These can be proved to be 0 and 1 respectively, using the definition of limits.

As for there only being one infinity, that is incorrect.

you guys are doing math equations. be simple no math use the <,>,= 1.0 is a whole number and 0.9999999... is not so therefore with NO MATH EQUATIONS it is not equal to 1. becuase 1.0 > 0.999999....... adding math equations it most likely will round it or actually make it so. but 0.9999999..... is not a whole number so it is not equal. Use simpler math like that.

.here are the reasons you requested. .9repeating is not one. .9 repeating is even
Y divisible by 3 while 1 is not. 1 is also evenly divisible by 5 while .3 repeating is not. The main "truths" for it are all flawed.

1/infinity=0 is not true. If you multiply both sides by infinity it ends up being 1=0 ehich is not true. (Unless someone asserts that 0(infinity) is one.

Finally: thr number of real numbers between 0 and 1 is less then the number of real numbers between 0 and 2. Thr number of real numbers between 0 and 2 includes both the amount of numbers between 0 and 1 and thr wmount of numbrrs between 1 and 2. I would gladly expand on any arguments.

1/3 = 0.333333333333333333333333333333333333333333333333333...
ANS * 3 = 0.99999999999999999999999999999999999999999999999...
ANS = 3/3 = 1

If you divide .9 repeating by 3 and 1/3 you would see that 1/3 would have a remainder while .9 repewting/ 3 would not. http://imgur.com/VivKpnD

1/3 does not equal .3 repeating.

x = 9/10 + 9/100 + 9/1000...
10x = 9 + 9/10 + 9/100...

10x - x = 9

9x = 9

x = 1

Don't knock the old mathematics caper, it's brilliant stuff.
I like the number i, which is the square root of minus one
completely imaginary, but essential.
I have been watching an excellent series on TV called "The Code"
I was discussing this with my elderly mother and we were discussing different number
systems, eg Decimal, Binary and Hexdecimal ( base or radex 16 ) when she piped up
with the info that mathematicians have another system that uses base 12
as in decimal 10 is only divisible ( in whole numbers ) by 5 and 2
whereas this base 12 caper is more useful because 12 is divisible ( in whole numbers )
by 3, 4 and 6
Has anyone else heard of it ???
Apparently there was an ancient civilisation in the general "Persian" area that
used a base 60 numbering system, derived from there astronomical "knowledge",
that they then used for "everyday" maths, symbols on clay tablets stuff.
I wonder if anyone has heard of that.
The romans might not have a digit to represent zero, and the idea of having a zero
is apparently from the Indian or Sri Lankan's

https://www.google.com/webhp?sourceid=chrome-instant&rlz=1CAASUB_enUS602US602&ion=1&espv=2&ie=UTF-8#q=.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999%2F3+*3

Deathllama: when you multiply anything by 10 you move everything to the left, (.99(10)=9.9) thrre is always one less number behind the decimal point, which would mean that when you subtract 10 x by x you would get a remainder.

Captainmeme is absolutely correct, but I'm not sure what the OP meant by "there is one infinity"

Ghug: i have not heard of that specific thing, but have thought that some numbers are very hard to write because of our current number system, and also came to the conclusion that a number system based off of 12 would be more practical.

I think when it comes to mathematics and logics, only personal opinion matters.

Cm: are you saying that they are equal to those, or that those would just be the limits which they would just become infinitesmally close to?

@tvr - I literally don't even understand what you're trying to say.

"1/3 does not equal .3 repeating."
I think I see the problem.

@tvr He essentially means both. Infinitesimally close is the same as equal to in almost every practical and theoretical application.

@igiv: that is not true though... If you wanted a number that was divisible by 9 with no remainder, .9 repeating would work, however, 1 would not.

@dl: i am saying that the problem with the 1/3=.3 repeating one is that it assumes that .3repeating is equal to 1/3 which, if .9repeating did not equal 1, would also not be true. I am also using the fact that 1/3 would have a remainder while .9 repeating/3 would not, and the fact that 1 is evenly divisibke by 5 while .3 repeating is not to show that they show very different properties and are therefore not the same number.
The second proof (x=9/10+9/100+9/1000) does not take into account the fact that when you multiply anything by 10 that you move the decimal point over and that the old last number is replaced with a 0. Ex: 9.9(10) becomes 99 . .37(10)=3.7 in both cases the number of significant digits behind the decimal point becomes one smaller. Because there is one less significant digit (science term) behind the decimal point, when you subtract it yields a remainder. Ex: 3.7-.37=3.33 . 99-9.9=89.1 . Do i need to try clarifying further?

"there's one infinite" could mean 2 things:

(1). There exists one infinite
(2). There's only one infinite

But if you assume OP meant what he wanted to mean, you must actually assume (1) AND (2).
In such case, Valis is right... till certin point: under USUAL AXIOMS (1) happens to be true, but (2) fails.

However, Valis is wrong when saying "there's no fucking debate" simply because you can (and it has perfect sense) to debate the axioms. It's famous, for instance, the 'finitist philosophy' and though I don't know at the moment of any philosophy arguing there can't be more than one infinite, there conceivably could be

This thread is infinitely stupid.

"i just don't like the idea of thinking of 0.99... as a number, since the number is 1. it's like -0. i don't like -0 as a number either." It's a matter of definitions ghug. If you don't like the USUAL DEFINITIONS, then you can go and invent your own maths.

And accordign to those usual defs and axioms, statement 3 is valid

@tvrocks: To address the "is .9 repeating equal to 1" question, you'll have to define what .9 repeating means. You might think that's just a question of common sense, but it really isn't.

Let's assume we understand what integers are (like 1) and fractions (like 0.9 or 0.99 or 0.999 but not .9 repeating). Real numbers are defined as infinite sequences of rational numbers like 3 - 3.1 - 3.14 - 3.141 - 3.1415 - 3.14159 - ... with one additional rule: two sequences are considered equal if their difference is q sequence which converges to zero.

So let's look at 1 and .9 repeating. 1 is the sequence 1-1-1-1-1-1-1-... and .9 repeating is the sequence 0.9 - 0.99 - 0.999 - 0.9999 - 0.99999 - ... The difference is 0.1 - 0.01 - 0.001 - 0.0001 - ... which indeed converges to zero. So .9 repeating is equal to 1.

Again Valis is right that statement 2 is 'nonsensical'... if we accept the usual defs, and it's simply cos 1/0 is not defined, as simply as that.

But again, you can perfectly 'force' a definition 1/0 := infinity, and it could have a many mathematical justifications

@ tvrocks: I think your confusion arises from the idea of significant digits. Real numbers have infinitely many significant digits. You might argue that we cannot measure any number with infinite precision and you'd be right. But to define real numbers, we have to assume that we can. If you insist on working with finite precision instead, use rational numbers and you'll never run into problems.

@tvrocks you'd do well reading some introductions to analysis, I think you could even enjoy them. I prersonally reccomend the Terence Tao "Analysis, Volume I" whhich first chapters you can download from https://terrytao.wordpress.com/books/analysis-i/ for free

@basvan: no matter how far you went it would not reach one. If .9 repewting ever actually did reach one, it would actually end up being bigger then pne as, because it is an ifinite series, even if it did reach one, it would still be adding more things on. In order for it to reach one without becoming bigger then one it would have to reach one and then stop which, because it is infinitely repeating, it does not have and would never stop.

I agree that number 2 is nonsensical, though take it 2 steps further to say that all of the statements are nonsensical. 1/0 is not infinity though as, unless 0(infinity)=1, it would be impossible to reach.