yes.
in reality - yes it does. does it make a difference - no.
so, are .999~ and 1 the same number?
in reality - no. does it make a difference - only on internet forums.
lol
here you go… any number multiplied by 1 is itself, right?
so, 1 x 1 = 1. 2 x 1 = 2. 5,837,279 x 1 = 5,837,279.
now try multiplying those numbers by .999~. can’t really do it. and even at your best approximation, the number comes back skewed in the decimal. at SOME point in the number, there will be a digit that is no longer 9. the same works with dividing by 999~.
you can’t use the argument that .999~ goes on forever and that would never happen, because unlike the math “proofs”, you can’t physically do the math and prove it.
lol I hear ya… I was honestly wondering if anyone knew the answer 
I was just curious
edit: ACTUALLY… I guess, if your not using 10 (aka start from zero and up opposed to starting from one) than that totally makes sense I guess. Because .999~ would be the highest number you could hit before going back to 0 (0,1,10,ect)
you arent going from
- x = -0.999…
to 9x = 9.000… = 9
you start with
10x = 10.999…
then you subtract x from each side, and get 9x = 9.000… = 9
edit: I dont want it to seem like me helping someone with the math to prove .99… = 1 means that I believe it. I still dont, and I still like my argument.
My favorite number is the number i…
10x = 9.99999…
You can’t do it b/c you can’t multiply on a traditional calculator by an infinitely repeating number…
Actually yes, in the sense that any machine using an IEEE 754 Floating Point Standard is wrong. Windows uses double precision or 64 bits to store a number in binary format. Since quite often mathematical operations exceed 64 bits in length there must be action taken to fit the number into a base10 representation of that value.
Option 1) chop the bit, like it never existed. Not used in IEEE 754.
Option 2) round the 64th bit, based on the 65th bit. In binary if the 65th bit is a 1 round up. This is what is used in IEEE 754 and leads to what is called cascading catastrophic error.
For a more in depth answer, look for my post here:http://www.nyspeed.com/forums/showthread.php?t=22279
ugh, i don’t want to get into this, but the correct answer would be circumstantial.
A little bit of engineering background first. Anytime something thats engineered and affects human safety has a “Factor of Safety” applied to it. A Saftey factor of 1 means that is the minimum design for load and a safe operation providing it’s a perfect world and there are no defects in material, workmanship, mother nature, etc.
That being said, If I were engineering a bridge that every one of you had to cross over would you cross it if you knew it only had a safety factor of .9999?
In my world, .9999 and 1 are a completely different.
Figures don’t lie and liars can figure.
Yes, .9999 and 1 are different. .99999… and 1 are not. You would not be able to use .9999… as written in your calculations, since you cannot terminate the expansion of the number and have it still be .9999…
To you, .9999… is useless. 1 is the representation you need and can use.
It does not EQUAL 1. It APPROACHES 1 as the number of decimals approach infinity. OK, now i’ll go back and read the whole thread to find out why that’s so fucking hard…
Oh sweet effing Jesus. You all are victims of a high school math teacher’s trick. Remember way back in the day when you had to check your algebra by doing it in reverse? Lets see if we can get back to .999~
x=1
9x=9
10x=10
10x-9x=10-9
x = 1
Oops! No .9999999~ in there. Your math doesn’t check out! :eyebrow:
It’s a cute trick but .999~ is a fucking number. It is a number that approaches 1 forever. It is not 1. It gets closer and closer and closer until the end of time but it is never equal to 1.
Agreed, the algebra is correct. Unfortunately, 1 simply does not equal 0.999… Like Spock Says, it’s Illogical. (Even though tricks with numbers seem to show it as equal). In calculus, i remember lines that became asymptotic to another line. So 0.999… is becoming asymptotic to 1, but will “never” reach it therefore 1 is not equal to .999… It becomes “Infinitely close” to 1, but never reaches it. It’s just that simple, no matter what algebraic tricks are played.
what about jedi mind tricks?
i’m not into scientology.
Where is the answer “It will land on the surface of Mars”?
fancy card and coin tricks?
or the trick where someone taps you on the shoulder on the opposite side… then you look, but theres no one there.
i bet that trick would fool you into believing
i agree with LAFENGAS and BikerFry
ive taken too many college level math courses to be convinced that .9999999999999 = 1
it gets ever so close to 1, but not quite.
ughh now u guys have me thinking about limit graphs and shit with empty spaces… ahhhhhhh horrible calculus flashbackss!!! make it stop!!!
…all better
That is where the “trick” or, as I like to call it, the mathematical error lies. That equation was not solved correctly. That equation cannot be solved for a real number.
9.99~ and .99~ both have decimal places that go on for infinity. They are not real numbers. 9.99~ - .99~ is not = 9. It is equal to a number infinitely close to 9, but it is not a real number.
So while this is a cute trick of algebra, it is based on one false assumption: That you can solve infinity - infinity and get a real number. You cannot, as infinity is not a real number.
http://mathforum.org/library/drmath/view/57069.html
http://www.galactic-guide.com/articles/8R69.html
cant we just agree that it doesnt equal one, but machines still arent “smart” enough to realize it?
And I do agree with you BikerFry that the algebra is a bit of trickery. However you saying that it isnt a real number is false. Any non-terminating infinitely repeating decimal is a rational number and therefore a real number.
You’re right. My terminology is incorrect. As you stated, a repeating decimal is actually a real and rational number:
http://en.wikipedia.org/wiki/Recurring_decimal
My little bit of research to verify the terminology also reinforced that the error in the “proof” is in (9.99999~ - .99999~) = 9. It is not correct, it is undefined.
See here:
http://en.wikipedia.org/wiki/Infinity#Undefined_operations
:word: No it’s not equal to 1. Yes for all practical purposes it can be treated as 1.