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Forums - General - 0.9999.... = 1.0

 

Are you convinced?

Yes 34 58.62%
 
No 20 34.48%
 
not sure 1 1.72%
 
Total:55
Soleron on 30 April 2013
dsgrue3 said:
Soleron said:
dsgrue3 said:
x = 2
x^2 = 4
x = +/- 2

Fuzzy math is fuzzy. This is why it doesn't sit well with me.

I understand it through Pezus' example with fractions, but this isn't an equation. It's just an assertion.

It isn't a proof at all.

Surely you admit -2 != 2?

you're not allowed to multiply or divide equations by x without handling the fact you just added/removed a solution. In this case the second negative solution is an artifact because you multiplied by x. This happens all the time in real physics problems and you can just ignore the other solution. There is a more formal way to deal with it in pure maths but I'm not practiced with it.

Right, but this isn't an equation which is my point. It's a declaration of a variable. There is no equation in the OP or my post which is why this type of "proof" is bunk.

His explanation doesn't contain any invalid steps. Yours does. Neither are formal proofs but no one here would understand the formal proof.



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Zkuq on 30 April 2013
MDMAlliance said:
Zkuq said:
MDMAlliance said:

Really, the hole I see is that if it eventually did hit one, there should also be an objective point where the switch happened.  I can also see why 0.999... is looked at "since it goes on forever, and there cannot be a number between 0.999... and 1, 0.999... has to be 1."  I understand that.  That doesn't change the fact that it isn't a fixed object in my perspective.  Infinity would have to be a fixed object, too.  

Do you think 0.999... is a number at all? Nope. If you think it is, then it is definitely a fixed object. There's also a difference between an infinite number of periods and infinity.  I do acknowledge their differences, but there are many ways where they function the same way.  Also, what do you have against the proof using the sum of a geometric series? Can you tell where it goes wrong? If it goes wrong somewhere, you can point out the exact spot where the error is and you can do it without geometric intuition.  I simply do not think that the equation is perfect, especially considering what its limitations are.  I have not taken math in over 3 years so I would really need to study this stuff and come back to it later in order to produce any realistic conclusions.

 

How do you even compare 0.999... and 1 if you don't think 0.999... is a number? How do you compare two entirely different things? What is it if it's not a number?

And finally: Have you ever tried deriving the sum for geometric series? First you do it for the first n terms which is fairly easy, then you take the limit n->infinity which is almost trivial in this case. The equation is perfect, there's no denying that. The steps required to derive the equation aren't high-level mathematics, they're fairly simple.



Soleron on 30 April 2013
MDMAlliance said:
...

When I say "theories," I was referring to the Axiom of Choice theorem. 

When one says anything in maths is "true", you're implicitly saying, "given this standard set of axioms", one of which is probably the axiom of choice. Even just saying 1+1=2 implies a bunch of axioms.

Of course you can construct a logical system in which 0.999... doesn't equal 1. It's just not meaningful because no one else uses it. In the one we use, it's the same thing. In the one we use, we assume the axiom of choice.



SuperMarioWorld on 30 April 2013
Zkuq said:
SuperMarioWorld said:
Zkuq said:
SuperMarioWorld said:

the step 'subtract x' is a trick. you are treating x as a constant not a variable. so when you say subtract x it means subtract 0.99999 therefore your proof doesn't really hold up mathematically. its a trick

x = 0.999... and therefore 'subtract x' is the same thing as 'subtract 0.999...'. You can operate on both sides of an equation; the form you operate on each side is up to you to decide as long as both forms are equal. Besides, your point about treating x as a constant instead of a variable doesn't make much sense. x is x and it has a known value; what's the problem?

Oh I get it. You're just trying to mess with us.


i'm not messing with you. the problem with his proof is he is treating x as a variable. but it is a constant as he has stated in the first step. you can't just suddenly decide x is a variable in the middle of a proof when he has stated it's a constant at the start of a proof. In a proof you must define x to a degree for example x is any positive integer. he defined x as 0.99999. nothing else. his proof is completely wrong.

http://en.wikipedia.org/wiki/User:ConMan/Proof_that_0.999..._does_not_equal_1 

If you think the proof is wrong, please do point out the step that's wrong and why. All you have is an ambiguous statement about what's wrong but if there's something wrong, you should point it out exactly because it's not obvious. What does a variable even mean to you? And what about the other proofs? Also, have you studied mathematics? Besides high school level, that is.


I did point out the wrong step in my first post mate. 



SuperMarioWorld on 30 April 2013
Jay520 said:
SuperMarioWorld said:

the step 'subtract x' is a trick. you are treating x as a constant at the start of the proof and a variable on the 'subract x' step. so when you say subtract x it means subtract 0.99999 therefore your proof doesn't really hold up mathematically. its a trick


I don't care what you call it x. I made X equal to 0.99... 

At that point, everything I did was done to both sides, meaning I didn't change anything. Look, I can do the same for any other number you can think of. Here, I'll do some examples just for you.

x = 5 given
10x = 50 multiply by 10
9x = 45 subtract x
x = 5 divide by 9
5=5 substitution
x = 12 given
10x =120 multiply by 10
9x = 108 subtract x
x = 12 divide by 9
12 = 12 substitution
x = (1/9) given
10x = 10/9 multiply by 10
9x = 1 subtract x
x = 1/9 divide by 9
1/9 = 1/9 substitution

etc, etc.

So please tell me why this wouldn't work for 0.999...

now do it for 1/8.

it will only work if x is a positive integer or x is 1/9. there is your flaw. therefore you just prooved 0.999999 doesn't equal 1.



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Jay520 on 30 April 2013
SuperMarioWorld said:

now do it for 1/8.

it will only work if x is a positive integer or x is 1/9. there is your flaw. therefore you just prooved 0.999999 doesn't equal 1.

yeah, no 

x = (1/8) given
10x = 10/8 multiply by 10
9x = 9/8 subtract x
x = 1/8 divide by 9
1/8 = 1/8 substitution

try again



Jay520 on 30 April 2013

Added a poll to get a look at what the VGC members think



fordy on 30 April 2013

Infinite can be classed as a non-exact value, since it's definition is "greater than than all exact values", yet any number to compate against infinite is exact value. For instance, many argue that x/0 = Infinite, based on the fact that as lim y-> 0 : x/y -> Infinite, but that's not the case. Take for instance the following two rules applied to fractals:

Rule 1: x/x = 1
Rule 2: 0/x = 0

In which case, which rule applies to 0/0?

0 has similar properties to Infinite; it's a number to represent "nothing" (ie. "something" to represent "nothing"). Early mathematics did not contain 0. You'll find that many problems of mathematics involving infinite are usually the result of a 0 being present.



MDMAlliance on 30 April 2013

I'm not going to reply here anymore, and the reason is because it is too much work to keep up with. I'll just make it simple for myself and just go with the flow.
even though I still have my own thoughts about this



SuperMarioWorld on 30 April 2013
Jay520 said:
SuperMarioWorld said:

now do it for 1/8.

it will only work if x is a positive integer or x is 1/9. there is your flaw. therefore you just prooved 0.999999 doesn't equal 1.

yeah, no 

x = (1/8) given
10x = 10/8 multiply by 10
9x = 9/8 subtract x
x = 1/8 divide by 9
1/8 = 1/8 substitution

try again

oops i'm sorry i meant -1/8. your proof only applies to postive numbers therefore has many holes in your logic. However i was mistaken it would only work with positive integers. cheers for that