dtewi said:
Theoretically, if infinity has no end, how is there zero at the end of it?
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i still don't see how people are convinced they can calculate with infinity
| skeezer said: What is the difference between a black cat and a black dog??? |
Probably the shape and size of a number of internal organs and their physical shape and size.
Let's apply that to mathematics.
If two number are not equal, that means that there is a number between them.
Is there a number between 1 and 0.999....., 0.9 repeating, .9-bar, 0.9 infinty or whatever the fuck you want to call it.
Or, what is 1 - 0.9999999999999999999999999999...........................................................?
Kimi wa ne tashika ni ano toki watashi no soba ni ita
Itsudatte itsudatte itsudatte
Sugu yoko de waratteita
Nakushitemo torimodosu kimi wo
I will never leave you
dtewi said:
Probably the shape and size of a number of internal organs and their physical shape and size. Let's apply that to mathematics. If two number are not equal, that means that there is a number between them. Is there a number between 1 and 0.999....., 0.9 repeating, .9-bar, 0.9 infinty or whatever the fuck you want to call it. Or, what is 1 - 0.9999999999999999999999999999...........................................................?
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0,0000000000000000.............................................................00000000000000000000.............1?
dtewi said:
Theoretically, if infinity has no end, how is there zero at the end of it?
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Exactly. Which is why 1/3 can't be expressed as a decimal.
1/3 ~= .3-bar, it is not 1/3 = .3-bar. Notice the ~, approximately.
Math is taught that way. Through Tri you're told it's .33333.... because it's not necessary to confuse students with the concept to measure triangles.
In calc, they use them so they can be expressed graphically. In Human terms, we would never be able to perceive the difference between 1/3 and .3333..... but that doesn't mean they are equal. They are not. They are approximately equal.
In applied maths (physics, economics, statistics) you always clearly indicate the ~.
When you're a college junior taking advanced number theory, you will see more. I think my previous posts explain it pretty simply though. You're a smart kid, one day you'll be able to pass it on.
@kane, for now, leave it as 1-.9-bar, round, or approximate the return to a fraction 3(1/3). If I saw it on a test, I would leave it as 1-.9bar
I would cite regulation, but I know you will simply ignore it.
Interesting wikipedia page for this;
http://en.wikipedia.org/wiki/0.999...#Proofs
Edit: The main problem with this arises with the concept of infinity, the number 0.(3) is identicle to 1/3 because of the infinite recursion. To claim that 0.(9) is always slightly less than one is to ignore the fact that this is an infinitely long sequence of numbers, there is no end.
Kane said:
i still don't see how people are convinced they can calculate with infinity |
It is easy. What is infity minus infinity? Zero! What is Infity times one infityth? One! Or alternatively, what is infinty divided by infity? One! What is infinity times 1? Infinty!
Kimi wa ne tashika ni ano toki watashi no soba ni ita
Itsudatte itsudatte itsudatte
Sugu yoko de waratteita
Nakushitemo torimodosu kimi wo
I will never leave you
steven787 said:
And when you get into number theory you'll find out why that is an oversimplification that we use to express numbers.
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I've taken all the Calculus, Analysis, Number Theory and Linear algebra I ever intend to ...
The problem with a decimal number system and the true nature of numbers is that when you're dealing with an infinitely repeating number (like certain rational and irrational numbers) and you represnet them using a fixed number of decimal places there are an uncountably infinite number of numbers between they number you're representing and the actual underlying number.
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