Think about it... how can you have 3 equal parts of an object? The decimate representation is impossible and one side always has to be bigger then the other. This is also why there is no such thing as 360 equal degrees in a circle as one degree has to be off by a little bit... There are no 360 numbers that will add up to 1 whole object either.
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Anonymous2006-12-16 23:21
>>120
So this thread's faggotry is not a valid expression?
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Anonymous2006-12-17 0:40
>>118
NO! .0999... does not equal 1. Look at it, it's not the same number it all. The former has an infinite number of digits; the latter is 1. That's it.
>>122
Finally someone with some common sense! I told my dumbass grade school math teacher the same exact thing when she tried to convince us that 2/4 = 3/6. What a load of bullshit, am I right?
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Luna2006-12-17 6:00
3+3+3=10 now. Perfect for my plans.
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Anonymous2006-12-17 7:02
>>122
0.999... equals exactly 1. proving this is trivial, and several proofs have been shown. the only proofs you've offered are "well, it doesn't *feel* right" or "common sense dictates otherwise". you can't rely on intuition in math.
x = 0.999...
10x = 9.999...
9x = 10x - x
9x = 9.999... - 0.999...
9x = 9
x = 1
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Anonymous2006-12-17 7:54
Okay, so 0.999... may be 1, but 0.999...0 is definitely a different number.
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Anonymous2006-12-17 8:02
>>128
except that "0.999...0" is a nonsense number, you can't have anything after an infinite number of 9s by definition.
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Anonymous2006-12-17 10:14
>>129
I suppose you could say .999...0=.999... - (lim 9*10^x as x->-∞)
which would still equal 1
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Anonymous2006-12-17 10:45
I suppose if everyone accepted that 0.999...9 and 1.000...0 are NOT the same number then we would all be fine. This bullshit is why we can't invent anything that has a lesser chance of fucking up. Instead of this, "Oh it's pretty close, we'll call it 1 even though it isn't," is fucking retarded. Now, lets prove this.
>>133
If there's a 0 after all of the 9's, then there isn't an infinite number of 9's. This bullshit is why you can't graduate junior high.
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Anonymous2006-12-17 11:57
>>134
It's like the interval [0,1]. There's an infinite amount of numbers following the zero, yet there's still a one at the end. Having an infinite amount of things does not imply that there can't also both be a beginning and an end.
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Anonymous2006-12-17 12:39
>>135
You can't _list_ infinitely many things followed by another. There's a difference between a set and a list. Don't worry though, I don't think I really understood this in junior high either.
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Anonymous2006-12-17 14:06
>>136
You don't need to list them, that's what the '...' is for.
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Anonymous2006-12-17 14:10
>>137
Somehow I'm not surprised that you don't even know what "list" means in mathematics. List = "injective function from the natural numbers."
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Anonymous2006-12-17 14:53
>>138
If you really want a function from the natural numbers, you could define it by saying all the even numbers evaluate to the first half of the list, and the odd numbers to the second half (in reverse order).
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Anonymous2006-12-17 19:45
>>139
Oh jesus this is like teaching a special ed class.
There is no "first half" of the natural numbers (which index the digits after the decimal of a decimal expansion), nor a "second half." Suppose, for instance, that {1,2,...k} was the "first half" of the natural numbers. Then this supposed "first half" has only finitely many entries, and thus cannot be put in one-to-one correspondence with the even numbers. If, on the other hand, the "first half" is 1,2,3,... (ie, all of the natural numbers), then the "second half" contains nothing since the first half contains all of the natural numbers.
This is math, not philosophy or art. Infinity (and in particular the cardinality of the natural numbers, which is of primary relevance here) is well and rigidly defined. Because of this, you cannot simply foist your misguided and idiotic beliefs on others unless you're willing to rigorously support them. Unfortunately this is something you are completely incapable of doing, since it's increasingly apparent that you have less of a grasp of formal mathematics than a even an average first-year undergraduate. In short, either find a new hobby or try to actually learn mathematics, since in your current state you're just another "flat Earth" nitwit.
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Anonymous2006-12-17 20:43
Suppose, for instance, that {1,2,...k} was the "first half" of the natural numbers. Then this supposed "first half" has only finitely many entries,
I was with you until this point; you seem to neglect the case where k=∞/2.
yes, its much better to think of infinity as "indeterminate", as there is no largest number, and that's what you seem to be denoting. in other words, ∞/2 has no meaning, since ∞ has no determined value.
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Anonymous2006-12-17 21:37
>>131
lawl. "it's pretty close"? it's EXACTLY 1. there's more than one way to represent a given number. it just so happens that 3 * 1/3 is one of the ways of expressing the number 1, and 0.333... is one of the ways of expressing 1/3.
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Anonymous2006-12-18 12:20
So, how about we make three cakes, one for everyone?
And the world had eternal peace.
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LordRiordan2006-12-18 14:26
Im glad you have all realized that dividing by 3 isn't as simple as it seems. Soon you will realize it's mathematical impossibility.
Perhaps it might be theoretically possible in real life if you don't count the existance of qdots, but its mathematically impossible to represent as well. 1/3 = .333..., 2/3 = .666...
3/3 = .999... It would seem illogical for it to add to one as one piece would be slightly bigger then the other and making 3 equal parts impossible.
Yea... base 3 will still give you the same problems. Try dividing by .9.
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LordRiordan2006-12-18 17:10
3 is equal to .9 porportionately compared to base 10 and base 3.
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LordRiordan2006-12-18 17:14
Sorry its .9999...., not 1 :p
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LordRiordan2006-12-18 17:19
I take that back -.- It is .9
Dunno why I thought it was .999...
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Anonymous2006-12-18 17:25
>>150
You're so distracted by your poor understanding of math that you got a fail get.
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LordRiordan2006-12-18 17:28
Re: 152 a simple miscalculation.
3 is equal to .9 porportionately compared to base 10 and base 3
Prove it wrong bitch.
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Anonymous2006-12-18 17:50
>>153
3 in base 3 is 10 you nitwit. God, what are you? A fifth grader? You don't even know what "base n" means but you're willing to sit here and debate like your opinion matters?
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LordRiordan2006-12-18 18:31
You are a fucking duche bag 154
.9 in base 3 corresponds to what number in base 10? Its the same fucking thing just a different way of representing it.
Gtfo n00b
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Coffin2006-12-18 19:50
127 has shown .999... equals 1. This is how math works, proof. Since 3*1/3=0.999..., it equals 1. Different bases don't come into the question.
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Anonymous2006-12-18 21:28
>>127
I must say, you've completely convinced me. I've been trying to find a loophole all day and I still can't. Congratulations.
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Anonymous2006-12-18 22:16
>>155
There is NO SUCH THING AS .9 IN BASE 3. There IS no digit 9. Jesus!
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LordRiordan2006-12-18 22:26
Re: 158
Oops. Theres still an equivalent.
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Anonymous2006-12-18 23:10
>>159
You said ".9 in base 3 corresponds to what number in base 10?"
.9 in base 3 is nothing. It doesn't exist. If you are talking about the base 3 representation of the base 10 number .9, that is 0.22002200...
Now, for everyone's sake, either make a point or quit failing, because it's completely apparent now that you are barely qualified to talk about first grade arithmetic, let alone actual mathematics.