Established Member
I am trying to see how well people at BABB understand this, because other forums seem to show most people have a poor grasp of this idea.
There is a correct answer to the question. When I posted this in another forum, it was really surpised at how most people answered. So now I want to see how people here accept the correct answer. The correct answer is they are exactly equal. There is no difference between the two.
Member
The way it was explained to me:
5/9=0.5555555555555......
6/9=0.66666666666..........
7/9=0.777777777777777....
8/9=0.88888888888..........
9/9=0.999999999999.......
5/5=1.000....
6/6=1.0000....
9/9=1.00000....
Banned
I voted no. I don't know why. 8-[
Established Member
Also:
1/3 = 0.3333....
0.3333.... * 3 = 0.9999....
Therefore, 0.9999.... = 1
Order of Kilopi
Irony is:
With Nine People, now having answered it, the Poll Numbers, ONLY EQUAL 99%!!!
8-[
Member
I'm going on what I was taught in Calculus. You must have two points to make a slope, so one point will be at x=1 and the other point will be the limit as x approaches 1, but never reaches it. Thus, assuming x approaches 1 from its lower side, x = 0.999999..., but does not equal 1.
Established Member
Actually according to Calculus it is equal to 1. 0.99999... can be written as a limit. That limit converges onto 1. Thus 0.999999... equals 1.Originally Posted by AliCali
Also the limit of x as a apporaches 1 is exactly equal to 1, not aproximatly 1.
Order of Kilopi
From the numismatic world:
Fineness: the purity of a precious metal measured in 1,000 parts of an alloy: a gold bar of .995 fineness contains 995 parts gold and 5 parts of another metal. Example: the American Gold Eagle is .9167 fine, which means it is 91.67% gold. A Canadian Maple Leaf has a fineness of .999, meaning that it is 99.9% pure.
Established Member
We are not talking about 0.999 but 0.9999999... a different number.
Order of Kilopi
Oh.
0.9999999~ infinite 9s
Member
Nope!
Established Member
Yep
I would imagine that anyone who thinks differently has not yet encountered first semester calculus.
Established Member
Or is an engineer. Frankly once you're over 0.51, to all intents and purposes you can round it to one. Why? Because it'll vanish into the measurement error when you actually build it....
Cheers
John
Established Member
1 is an integer
0.9999999999~ is a real number.
they are not equal.
Order of Kilopi
Integers are a subset of real numbers. 0.999999~is just a weird way to write 1.
If I ask if π = 3.14159..... you can also not say: No, π is a greek letter and 3.14159....... is a number, so they are not equal.
Banned
ops:
Would anyone be equal to Candy?
Order of Kilopi
Another way to think about it is to consider the difference between 1 and "0." followed by n 9s. The difference for finite n is given by 10^-n, so in the limit n->infinity, the difference between 1 and 0.9999... tends to zero, hence they are identical.
Established Member
1 is used in binary (or any other base you care to name), and logic where 0.9999999~ is meaningless. Ok, maybe it's semantics but 0.999999~ is not equal and alike to 1 in all respects.
I do accept that the series (9*10^-1 +9*10-2 + ... + 9*10^-n + ...) >1 as n>infinity but this is only true (= 1) for base 10 calculations.
There is a wider world out there we should all be aware of.
Banned
Like when the ~Sumerians didn't have the number 0? 8-[
Established Member
I don't think it is equal becuase it istn't. It is close though, and would be acceptable to round... espicially since you have infinate 9s.
Insert awesome title here
Yes. If you don't agree, just ask yourself what you would get if you substracted 9.99999999999999........ from 1.
Established Member
-9?
Insert awesome title here
Exactly, which is the same thing as 1 subtract 10 therefore they are equal.
Established Member
nice cover
Banned
That's exactly what I presume the Sumerians said. :-k
I hope with string theory, there is a whole other world opening up to us.
Back to math as we know it.
VVV
Established Member
they are equal. A real number is defined as the limit of a sequence. If two sequences have the same limit, then both of them define the same number.
So there.
Order of Kilopi
It's as close as you want and so there is no need to round to make it equal to 1.
But this here is a nice excercise on how diffcult it is to grasp the significance of what "limit" means. Am I correct when I say, if 0.9999~ would be not equal 1, then the whole calculus would fall into shreds?
Harald
Established Member
Close? Close?!?
You understand the concept of infinity, right?
Order of Kilopi
[strikeout]It depends.
Mathematically, they are quite different, but in the real world, the difference is so minor as to be irrelevant.[/strikeout]
In computing, the difference depends on whether your ALU rounds or truncates "infinite" floats.
[edit:] I think jfribrg just sold me. They are the same, mathematically, although the why is not an intuitive thing to grasp, I think.
Established Member
Sure, for small enough values of 1.
:P :P :P :P :P :P
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