I'v had in-depth conversations about this on many occasion. Just wondering what you guys have to say . . .
I NEED TO KNOW!
I NEED TO KNOW!
Poll: Does 0.999.. equal 1 ?
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1/3 = 0.333...
0.333...*3= 0.999...
on a different calculator
1/3 = 0.333...
0.333...*3= 1
Mathematics is flawed
0.333...*3= 0.999...
on a different calculator
1/3 = 0.333...
0.333...*3= 1
Mathematics is flawed
No. = means that both sides are identical. Identical means that there is no difference at all. Not no difference except a difference infinitely small. A difference is a difference. 0.99999999999999... is not 1. If it was, it would not exist we would simply write 1.
Not to be rude, but since when has 9/9 ever equaled .999...?
Everything up to that does turn out 7/9=.77777 ect, but unless everything taught in school is wrong, a number divided by its self will always equal 1.
Everything up to that does turn out 7/9=.77777 ect, but unless everything taught in school is wrong, a number divided by its self will always equal 1.
EXACTLY if it was the same then it would just simply BE THE SAME and would therefore be 1tzimize said:
Yes, it does and don't listen to anyone who says otherwise. Math does not allow personal interpretations.
0.(9) exactly equals 1, always, without a shadow of doubt. 0.(9), 0.999..., 1 are just different ways to write the exact same number, 1.
Here's the wiki. It has various proofs and answers to misconceptions. [http://en.wikipedia.org/wiki/0.999...]
0.(9) exactly equals 1, always, without a shadow of doubt. 0.(9), 0.999..., 1 are just different ways to write the exact same number, 1.
Here's the wiki. It has various proofs and answers to misconceptions. [http://en.wikipedia.org/wiki/0.999...]
Mathematics is a language, and such it has to take certain liberties to express abstract concepts. It depends on your base counting method. You can't make an exact third of 1 in base 10 in real numbers, so .99~ is equal to 1, and there are proofs to back it up. If you're counting in base 3, then it's very easy to make a third, but similar problems to .999~=1 arise, when dealing with other numbers.
But if you're asked by a mathematician in that field if .999~=1, then you're going to have to deal with it if you want to get by.
But if you're asked by a mathematician in that field if .999~=1, then you're going to have to deal with it if you want to get by.
No it isn't. It has an asymptote at 1, so 1 is a value it will never reach, no matter how many nines you add. Even infinite nines would in principle leave it an infinitely small amount short of 1.
Also, this is flawed. Math gets pretty exact, but that doesn't make it universal law. They way that we work math allows for some stupid loop holes, like 1/3=.3333... but 3/3 doesn't equal .9999...Spencer Petersen said:
Its all a part of not being able to properly express a value with the decimal system alone, which is where fractions come in IMO.
If it doesn't work, how can we calculate with integrals (and differentials)? Those calculations are based about exactly that.GundamSentinel said:
Untrue. It goes 0.999... on to infinity. You'd think logically, you would just add a number that went 0.000...1. However, you can't have a 1 at the end of an infinite number of zeros, for that assumes there is an end to infinity, which there isn't. In mathematics, everything needs to be proven, and all the proofs say that 0.999... = 1. Whether you use rounding, limits, or just absolute practical value, they are identical.ZiggyE said:
Also, you have to remember that such a number would be identical to a level so infinitely small that no physical measurement could possibly amount to it. The decimal limits go down to a point that is smaller than any subatomic particle, and therefore, non-existent for any argument.
Again?!?!?!?!
Yes, of course they're the same. You've got proofs coming out your ears if you're willing to look, but basically if you think infinitesimal is a thing in math you're wrong. If you think there's something at the end of infinity you're wrong. If you think infinitely small is somehow different from zero you're wrong. If you think every unique number has it's own single unique representation with no overlap or redundancy you're wrong.
If you take 1 and subtract 0.999... from it the difference is 0.000...
The zeros repeat forever. Not until the end of infinity where nine minus nine somehow magically equals something different. FOREVER. 0.000... with zeros going on forever is the same thing as 0. There is no difference.
Yes, of course they're the same. You've got proofs coming out your ears if you're willing to look, but basically if you think infinitesimal is a thing in math you're wrong. If you think there's something at the end of infinity you're wrong. If you think infinitely small is somehow different from zero you're wrong. If you think every unique number has it's own single unique representation with no overlap or redundancy you're wrong.
If you take 1 and subtract 0.999... from it the difference is 0.000...
The zeros repeat forever. Not until the end of infinity where nine minus nine somehow magically equals something different. FOREVER. 0.000... with zeros going on forever is the same thing as 0. There is no difference.