ok so i think we've hit on the issue, then. i've always said -0 doesn't exist. because it's redundant.

0.1111..... = 1/9; 0.1111..... * 9 = 0.9999..... = 9/9 = 1.

Q.E.D

I see. Well, it does. It's not redundant, because it's not a different number from 0. It's the same number. It's like you're not redundant even though you (presumably) have both a first and a middle name.

in my opinion, you can't say 0.99... exists as its own number unless you are CERTAIN that it is unique. otherwise, it's just an infinite sum. but since we know 0.99... = 1, then there is no number 0.99..., the number is 1.

ok whatever, maybe my view isn't the view of mathematicians, but that's the way i've thought about it.

Because personal opinion counts when it comes to mathematics.

my definitions feel more consistent to me. and this is not mathematics we're talking about. mathematics is about assuming definitions, then drawing conclusions from those definitions. there are more popular and less popular definitions, and mathematics doesn't rank which are better or worse, that's just the community. and the math community can suck it.

Well, bolshoi, those are nice thoughts, but I must say, I expect your definitions actually AREN'T consistent, and wouldn't work well in practice at all, if you actually did any math. :-) That's why the math community's definitions should be preferred.

For example, if you do any algebra, then if you used your definitions, you couldn't multiply both sides of an equation by -1 unless you were sure that it wasn't zero, which would be very tedious.

that's not true. the math would be the same, it's just that i wouldn't call those intermediate steps numbers, but expressions that need to be evaluated to a particular number.

(An additional issue is that if you just say words about something -- for example, if you refer to zero -- then people will assume that you mean the standard, accepted definitions. As a mere matter of communication, therefore, having one's own axioms of mathematics, inconsistent with the math community's, is most inconvenient. Of course, you could just say "my zero.").

Right, but then you couldn't demonstrate that the steps were correct. The standard proofs of such things assume the standard definitions of the objects involved. If you change the definitions, you can't just assume the standard theorems all still apply and that you're consistent. You're probably not.

When you say "the math would be the same" -- well, "the math" assumes we're manipulating numbers all through, so it most decidedly would not.

hm... i don't know. if i use the same theories then i'm pretty sure people will know what's going on. whether i call something a number or an expression should not throw off any legit mathematician.

the only real difference is that i say it's an expression that represents a number, but you say it's just a number. to be honest i'm not even sure you are more in-line with the community's definitions, but even if you are, it shouldn't matter.

No, you say it's an expression that does NOT represent a number.

depends what you mean by represent. an infinite sum to me cannot be called a distinct number until you know that it's not a number you already have. all the infinite sums evaluate to some number, but it's not a one-to-one ratio.

if you call infinity a number. but i guess you wouldn't given your orthodoxy.

I didn't say it was a distinct number. I said it was 1.

0.99... is distinct from 1. if you look closely you can tell.

As sets of symbols, yes. As expressions, yes. But as numbers, no. They both represent the same number. Many proofs have already been given. That you still deny such shows that, in fact, you do NOT operate by the same (correct) rules of math; if you did, then zultar's correct algebra in his first post would have convinced you.

if you've been online all this time you should have joined a live game! hours ago we were at 6 people. ok well again i didn't say .99... doesn't represent 1. i said it isn't 1. there's a difference.

and a side-argument, how do you know he necessarily meant 0.99... has an infinite number of digits, maybe he just meant an arbitrarily high number of digits.

ok maybe "represent" isn't what i mean. but whatever it is, i'm still saying 0.99... is not the same thing as 1.

The rigorous definition of the string of symbols "0.999..." is the limit of the sequence 0.9, 0.99, 0.999... This limit is 1. So inasmuch as "0.999..." has any meaning it is in fact equal to 1. This is the mathematicians view. Philosophers may disagree but they will have to give a different definition of the string "0.999" I think there may be an alternative view provided by a field of mathematical logic called "nonstandard analysis" Nonstandard analysis was invented in the 1960s and it makes use of "infinitesimals" which are nonzero elements which are smaller than every positive real number. I dont know much about it but maybe you could define .999... to mean 1 minus an infinitesimal in which case it would in fact be different from 1.

It's not 1 but it's very close.

philosophers may disagree, but most mathematicians are philosophers.

Both are disciplines which only require thinking. Mathematics is a very specific kind of thinking, but it is still philosophy, or perhaps it can be defined as 'useful philosophy'

How is this thread still happening?

Look I'll break it down for you. There are people who are right (Zultar, Semck), and people who don't know enough math to deserve an opinion (anybody who disagrees with them).

I withdraw any and all criticism(s) I have made of Ghug
and also apologise for any assumption(s) I have made as to the meaning of MM
referring to myself.
MadMarx was here first & has a higher ranking than myself
maybe y'all could use MM for MadMarx and mm for myself,
because MadMarx does not equal MajorMitchell,
the correct mathematical expression might be
MadMarx > MajorMitchell ( the symbol > meaning "greater than" )
a simple yet elegant expression

And MajorMitchell is definitely NOT a multiaccount / subsidiary / alter ego /
reincarnation or facsimile of MadMarx
perhaps y'all could use MM> for MadMarx (the greater )
and mm< for MajorMitchell (the lesser, dare I say, of two evils ) just kidding MM>

if PresidentEden is /was a multiaccount of obiwanobiwan and the Moderators
will / have closed the PresidentEden account,
do they also shutdown the obiwanobiwan account ?

I took the trouble to read the "mathematical proofs" for 0.99999 recurring equals 1
and accept them as valid (probably should have done that earlier )
my favourite number system is Hexdecimal, radex 16 digits, mainly because it makes
binary easier for my clockwork brain to comprehend

@bol

What is your background, if you don't mind me asking? Are you a HS student? A college student? An art history major? A computer scientist?



Here's the thing about math: It's all built off of simple definitions. The beauty is, if you know the starting point, you can rederive all of math from all history. But, if you start making your own definitions, you're going to have problems.

So, let's look at some definitions:

What is the mathematical definition of zero? Under the operation of multiplication, 0 is *defined* as:

0*n=0

What is the definition of -n? It is *defined* as shorthand notation for (-1)*n.

So, what is -0? It is nothing more than shorthand for (-1)*0. Since n*0=0, we know (-1)*0=0. This is no more redundant or odd than 5*0=0 or (-3)*0=0. It just is what it is.