It does equal ten actually, but you have to remember that what you're doing is the sum of a series expansion. I'll try to write it out, but I don't know how well it's going to work without series notations and such.
3.333333...=3+(3/10)+(3/100)+...
Thus it is the sum of an infinite geometric series. We can calculate that sum rather easily by the formula:
S=a/(1r), where in this case a=3 and r=1/10. There fore
S=3/(1(1/10))=3/(9/10)=30/9=...
So not surprisingly 3.33333...=10/3, and if we multiply by 3 we get 10.
The problem is that if you leave it in decimal form, you're truncating, cutting off, the series, at some point. The more terms, or the farther along you make that truncation, that you use, the closer you'll get to 10 in this operation, but you still won't quite get 10 because you haven't summed over the entire series.
Does your head hurt yet? Mine sure does. I hate this series expansion crap. :(
If 10 divided by 3 is equal to 3.3333infinity, then why isn't 3.333333infinity times 3 10?
Chris [Ninja]™
2008/08/21 19:04:14


11 votes


37%  
8 votes


27%  
11 votes


37% 
Or you could say, if:
x = 10/3
x*3 = 9.9999999999to infinity but does not every REALLY equal 10.
x = 10/3
x*3 = 9.9999999999to infinity but does not every REALLY equal 10.
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Icedragon1969 2008/08/21 21:49:43Well...
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same thing with apples you would eventually end up to atoms
No, you don't add a 1 at the end of the 0 because it's never ending, and if you added a 1 it wouldn't be.
because thing that are infinate are beyond human comprehension (explanation) 9.999999infinatly will go on infinatly evetualy the human mind canot umderstand it making 9.999=10 (this is pure opinion stated as fact)
Man, I'm not going to think much more than that ~ my head will blow up otherwise..
because 3 .3333 infinity cant be multiplied or divided by any number no matter who tells you it can, you can only give a reference to an idea of an probablity of exactness by using a number like 3.333 and adding a bar  .
Good luck with it.
get it?
3.333333...=3+(3/10)+(3/100)+...
Thus it is the sum of an infinite geometric series. We can calculate that sum rather easily by the formula:
S=a/(1r), where in this case a=3 and r=1/10. There fore
S=3/(1(1/10))=3/(9/10)=30/9=...
So not surprisingly 3.33333...=10/3, and if we multiply by 3 we get 10.
The problem is that if you leave it in decimal form, you're truncating, cutting off, the series, at some point. The more terms, or the farther along you make that truncation, that you use, the closer you'll get to 10 in this operation, but you still won't quite get 10 because you haven't summed over the entire series.
Does your head hurt yet? Mine sure does. I hate this series expansion crap. :(
It's the reaction of a lot of people. It seems to me to come about because we live in a truncated, finite world, so many can't see past that. Try and explain to most people how there can be different sized infinities. ;)
I also have experience with the fact that most people don't seem to understand that we humans invented math, that it is not intrinsic to the universe.
http://www.rpi.edu/~newbel/mi...
You make an excellent point that all numbers are concepts, however, which I did not give adequate thought too in my last post. I think engineers and others who use mathematics daily to describe the physical world would agree with your view, and those in the humanities or philosophy would agree with my "philosophical mathematics" viewpoint. I have to thank the author for this post. What an interesting thing to think about.
9 + 9/10 + 9/100 + 9/1000 + ... 9/10^i
Converges to 10 in the limit when i goes to infinity.
x = 9 + 9/10 + 9/100 + 9/1000 ... 9/10^i (i goes to infinity)
so: x/10 = 9/10 + 9/100 + 9/1000 ... 9/10^i (i goes to infinity)
x  x/10 = 9
so x = 10