Post me your hardest maths question you know
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0.99r *shudder*
Decimals and mathematics don't mix
0.99r = the sum of 9/(10^n) from n = 1 to m. Where m is a natural number
1 - the sum of 9/(10^n) from n = 1 to m is just 1/(10^m)
So for every m 1 - (0.99r) is not equal to zero.
Although the LIMIT or the sum of 9/(10^n) as m tends to infinity is 1. Although in real terms this limit cannot be reached.
Case closed.
Decimals and mathematics don't mix
0.99r = the sum of 9/(10^n) from n = 1 to m. Where m is a natural number
1 - the sum of 9/(10^n) from n = 1 to m is just 1/(10^m)
So for every m 1 - (0.99r) is not equal to zero.
Although the LIMIT or the sum of 9/(10^n) as m tends to infinity is 1. Although in real terms this limit cannot be reached.
Case closed.
How can you not accept it? It's a fact.
I love this thread - there's one side of the argument claiming that 0.9r is 1, and are offering mathematical explanations for it, and there's the other side which claim as it goes against their intuition it must be witchcraft. 
Soldato
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I love this thread - there's one side of the argument claiming that 0.9r is 1, and are offering theoretical explanations for it that can not be applied to the real world, and there's the other side which claim as they live in the real world it must be witchcraft.
Fixed for you.
Fixed for you.
You're making a distinction that no-one else makes.
Here's another one: the decimal form of 1/9. What is it? Both theoretically and in the 'real world'?
I hope one day we meet, and you have a cake. I will ask if you want all three thirds of it, and upon receiving confirmation, I shall take a bite which I will later claim to be infinitely small, and then show you this thread. 
I don't understand how people keep saying this 0.9r =1 stuff is so theoretical and doesn't exist in the real world... How is that at all relevant?
From Wikipedia:
The equality 0.999... = 1 has long been accepted by mathematicians and taught in textbooks. In the last few decades, researchers of mathematics education have studied the reception of this equality among students, many of whom initially question or reject it. The students' reasoning for denying or affirming the equality is typically based on their intuition that each number has a unique decimal expansion, that nonzero infinitesimal numbers should exist, or that the expansion of 0.999... eventually terminates. These intuitions fail in the real numbers, but alternative number systems can be constructed bearing some of them out. Indeed, some settings contain numbers that are "just shy" of 1; these are generally unrelated to 0.999...
Essentially Lightnix and and Amleto have both proved it nicely in different ways. It really is just intuition that is the reason for some people not accepting it.
From Wikipedia:
The equality 0.999... = 1 has long been accepted by mathematicians and taught in textbooks. In the last few decades, researchers of mathematics education have studied the reception of this equality among students, many of whom initially question or reject it. The students' reasoning for denying or affirming the equality is typically based on their intuition that each number has a unique decimal expansion, that nonzero infinitesimal numbers should exist, or that the expansion of 0.999... eventually terminates. These intuitions fail in the real numbers, but alternative number systems can be constructed bearing some of them out. Indeed, some settings contain numbers that are "just shy" of 1; these are generally unrelated to 0.999...
Essentially Lightnix and and Amleto have both proved it nicely in different ways. It really is just intuition that is the reason for some people not accepting it.
Because it's not being honest and misses a pretty important issue, the calculation itself, you can come up with any old calculation but just because you write it down doesn't mean you're magically given the answer, it takes work to do calculations.
If we wanted to calculate it we either need infinite time or an infinitely powerful computer, considering we don't have either the calculation will never be done and couldn't anyway because it deals with infinity.
Take the square root of 2. This is irrational, so it has an infinite decimal expansion.
Your argument is like saying that we can't multiply the square root of 2 by the square root of 2 because we'd need to do a calculation involving an infinite amount of digits. I'll tell you what the answer is. It's 2. I know this because I can look beyond the decimal expansion of a number and interpret our notation for what it actually means.
0.9r doesnt = 1
1=1
No matter how close you get to 1 with 0.9r. It will never hit 1 until you round up. As said, if you are dealing in theoretical maths then fine but there is no way that you can say that 2 different values are the same.
As mentioned, recurring means that the value is infinite beyond that point. You will just be getting down to a smaller and smaller difference between values but that won't ever hit 1.
If you could break distance down into an infinite unit that would accomodate infinite decimals then you would never travel 1m by travelling 0.9r meters.
1=1
No matter how close you get to 1 with 0.9r. It will never hit 1 until you round up. As said, if you are dealing in theoretical maths then fine but there is no way that you can say that 2 different values are the same.
As mentioned, recurring means that the value is infinite beyond that point. You will just be getting down to a smaller and smaller difference between values but that won't ever hit 1.
If you could break distance down into an infinite unit that would accomodate infinite decimals then you would never travel 1m by travelling 0.9r meters.
Like i said it's fine if you accept that what you're doing amounts to mathematical trickery but doing such calculations in reality is impossible due to the infinity issue.
DERP
By the exclamation mark do you mean factorial? because if you do then thats some serious fail there.
6! / 2 is NOT equal to 3!
and so 0.9! / 9 is NOT equal to 0.1!
And if you aren't using the ! to mean factorial then idk why you have it there.
I'm using != to mean not equal to, because I don't have a key with an equals sign that has a line through it.
!= is the general expression in programming for not equal to.