dream431ca
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Ikerous said:
Oops..didn't realise it..thanks.
0.999.... = 1
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Oops..didn't realise it..thanks.
@ dream431ca :
I appreciate that you're in the industry, and that if you get an answer of .99999 volts when you're aiming for 1, that's bad. This is has nothing to do with the math, though, since it's true that .99999 <> 1.
You keep saything "there's an error." Could you tell us exactly how much error? What is the distance between 1 and .999repeating? For any number greater you give that's greater than zero, it's not hard to see that .999repeating is even closer to 1 than that number. Since the distance isn't greater than zero, it must be equal to zero (since distances can't be less than zero).
@ the guy who says math's illogical
The weird thing about that is that math is absolutely nothing but logic. It's probably the only field that can't actually point at something and say "this is what we study," since numbers, functions, and sets can't really be pointed to. The way things are defined in math are really rather arbitrary.
If you'd like, you could define a real number as "a sequence of finitely many digits {0,1,2,3,4,5,6,7,8,9} followed by a decimal point followed by a potentially infinite sequence of digits {0,1,2,3,4,5,6,7,8,9}" and say that two reals are equal if and only if every digit in both sequences is equal, with the exception of leading and trailing zeros. You could study these things you call real numbers and notice things like .9repeating <> 1. This scheme fails to be a field, however, which is an important property that we'd like real numbers to have.
That is, of course, not at all a standard definition of the real numbers. Standard equivalent definitions include the real numbers are "the complete ordered field" (you then must show that there's only one complete ordered field), or "equivalence classes of Cauchy sequences of rational numbers such that two Cauchy sequences are equivalent if and only if, under the assumption that Cauchy sequences must converge, those two Cauchy sequences must converge to the same value."
I was going to say more, but I'm rambling and have to go talk my clothes out of the washer now.
I appreciate that you're in the industry, and that if you get an answer of .99999 volts when you're aiming for 1, that's bad. This is has nothing to do with the math, though, since it's true that .99999 <> 1.
You keep saything "there's an error." Could you tell us exactly how much error? What is the distance between 1 and .999repeating? For any number greater you give that's greater than zero, it's not hard to see that .999repeating is even closer to 1 than that number. Since the distance isn't greater than zero, it must be equal to zero (since distances can't be less than zero).
@ the guy who says math's illogical
The weird thing about that is that math is absolutely nothing but logic. It's probably the only field that can't actually point at something and say "this is what we study," since numbers, functions, and sets can't really be pointed to. The way things are defined in math are really rather arbitrary.
If you'd like, you could define a real number as "a sequence of finitely many digits {0,1,2,3,4,5,6,7,8,9} followed by a decimal point followed by a potentially infinite sequence of digits {0,1,2,3,4,5,6,7,8,9}" and say that two reals are equal if and only if every digit in both sequences is equal, with the exception of leading and trailing zeros. You could study these things you call real numbers and notice things like .9repeating <> 1. This scheme fails to be a field, however, which is an important property that we'd like real numbers to have.
That is, of course, not at all a standard definition of the real numbers. Standard equivalent definitions include the real numbers are "the complete ordered field" (you then must show that there's only one complete ordered field), or "equivalence classes of Cauchy sequences of rational numbers such that two Cauchy sequences are equivalent if and only if, under the assumption that Cauchy sequences must converge, those two Cauchy sequences must converge to the same value."
I was going to say more, but I'm rambling and have to go talk my clothes out of the washer now.
dream431ca
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You are right on the money with that post...like I said before..industry and Mathematics are not the same when it comes to 0.999 and 1. The industry treats it differently than mathemeticans (bad spelling). What do you mean I say there is an error?? you mean in the mathematics or in my industry post?? If it is my industry post, your talking about a microchip not understanding what 0.999 is. It only understands 1 - 1.3 volts not 0.999. Therefore an error will occur in the system if it does not equal to 1 or 1.3. Mathematics and industry are 2 very different realms.
dream431ca said:
When I was referring to "error," I was referring to your usage of the word in your post. If something says .999 and is supposed to be 1, there's an absolute error of .001 . I was informally talking about epsilon.
I don't understand why you say math and industry don't agree on .999 vs 1. They do. They agree that .999 and 1 are very different numbers. .999 < 1 . Period.
The difference is that industry almost never uses repeating decimals, while math occasionally does.
The problem is that we've gone on forever about is that .999 is not the same thing as .999-repeating-forever-and-never-ever-ending. Mathematics and the industry also usually handle this the same: write it as "1" since it refers to the EXACT same number, but is a lot shorter to write and easier to work with.
sinkoman
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Ikerous said:Thats cuz two different numbers can't be equal
However, .9 repeating and 1 are the same number in different forms
How so? .9 repeating is .9 repeating. 1 is 1.
I fail to see how they are the same number in different forms. How can a number be same but in different form.
Top Secret
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sinkoman said:
Go get a math book. =)
It's funny, after my math teacher taught us this, I walked up to the board and wrote 1.0x1 = 1 (Where X equals infinity.) Yeah, it was geeky.
15357
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sinkoman said:
0.33333333....... = 1/3
1/3 = 3/9
0.333333333..... * 3 = 0.9999999.....
3/9 * 3 = 9/9 = 1
Since 3/9 = 0.3333333..... and its both multiplied by 3, 1 and 0.99999.... are the same.
Probably been posted. Too lazy to read all of thread.
sinkoman said:
That's true. .9 repeating is .9 repeating and 1 is 1. It's also true that 1 is .9 repeating. Tell me, what's the average of .9 repeating and 1?
sinkoman said:
Hey look!
0 = log 1 = sin(pi) = 0/100 = 0% = lim (n -> infinity) (1/n) = 1 - 1
Wow! That's like 7 forms of the exact same number!
No wait... they don't look the same. I must have made a mistake somewhere...
EC
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Ok, since some of you don't like clicking links, here's an easy-to-understand simple algebra way of explaining .999... = 1.
(.99... == .9(infinity))
x = .99... Multiply both sides by 10 and you get
10x = 9.99... If you subtract 1x from each side (moving it to the right side) you get
9x = 9.99... - x Full in the 2nd x with the original statement
9x = 9.99... - .99... And do the subtraction
9x = 9 Simple algebra
x = 1.
(.99... == .9(infinity))
x = .99... Multiply both sides by 10 and you get
10x = 9.99... If you subtract 1x from each side (moving it to the right side) you get
9x = 9.99... - x Full in the 2nd x with the original statement
9x = 9.99... - .99... And do the subtraction
9x = 9 Simple algebra
x = 1.
TheSomeone
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Emm DoubleEw (10:02:20 PM): Isn't it wierd how all of a sudden all the people who agree that .9... = 1 are posting?
Emm DoubleEw (10:02:25 PM): You know what my theory is?
Emm DoubleEw (10:02:28 PM): Bedtime...
Tw33k3l2 (10:02:35 PM): XD
I'm EmmdoubleEw, Tw33k3l2 is Ikerous.
Emm DoubleEw (10:02:25 PM): You know what my theory is?
Emm DoubleEw (10:02:28 PM): Bedtime...
Tw33k3l2 (10:02:35 PM): XD
I'm EmmdoubleEw, Tw33k3l2 is Ikerous.
Orcone101 said:
Let's find out:
Fact 1) TheSomeone is right concerning this particular issue.
Fact 2) There is exactly one right answer concerning this particular issue.
Let S = {people who agree with TheSomeone}.
Let T = {people who are right concerning this particular issue}
S is contained in T, since every person in S agrees with TheSomeone (by definition), who (by fact 1) is right concerning this particular issue, everybody in S is right concerning this particular issue, and is therefore in T.
T is contained in S, since every person in T is right on this particular issue (by definition), and therefore agree with TheSomeone on this issue (by facts 1 & 2), and are therefore in S.
Therefore S = T.
Complementing both sides yields:
Not S = not T.
Therefore: If you do not agree with TheSomeone, then you are wrong.
So yes, in this case, that logic applies, but not a priori.
TheSomeone
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15357 said:Or perhaps most of the relatively smarter people who haven't skipped first grade live in different time zones.
You mean like the republic of HL2.net?
Qhartb said:
Best post in this thread so far.
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