TheSomeone
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Qonfused said:
Yeah seriously, I deserve an award for this spamfest.
0.999.... = 1
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Yeah seriously, I deserve an award for this spamfest.
Raeven0
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I reason philosophically that they're different by some infinitesimal value.
Interesting but completely useless morsel of knowledge: there are more real numbers between 0 and 1 than there are natural numbers, even though both are infinite sets.
Interesting but completely useless morsel of knowledge: there are more real numbers between 0 and 1 than there are natural numbers, even though both are infinite sets.
TheSomeone
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dream431ca said:
No he isn't at all, 0.999... isn't a function, it's a constant. How can you even compare the two?
TheSomeone
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Raeven0 said:
That makes no sense...
dream431ca
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WhiteZero said:
Infinite is an expression..not a number..mathematics has a huge problem with infinite...even though it's used in various applications, it just means something EXTREMELY BIG or EXTREMELY small...it cannot represent an actual number, just a expression.
TheSomeone
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Pesmerga said:
How many feminists does it take to screw in a lightbulb?
1 to screw it, 1 to lecture about how the lightbulb is being exploited, and another one to wish she was the lightbulb.
TheSomeone
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bvasgm said:
Too bad every single math professor in the world agrees with me.
dream431ca
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TheSomeone said:
Because a function uses numerical and consecutive constants and plots on a graph..what he is saying is that 0.999 will never equal one (mathematically) it's just displayed on a graph.
TheSomeone
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WhiteZero said:
Pure boredom and lack of funds for DOD: Source.
Do you pity me now ;(.
spookymooky
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What shape is that? We never did that in calc ABIkerous said:
TheSomeone
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About the initial flame, I was just starting a fire with 12 gallons of burning alcohol, I didn't really mean it. You have to admit the thread grew faster than a penis on viagra.
TheSomeone
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spookymooky said:What shape is that? We never did that in calc AB
A klein vase?
I'm just guessing, I haven't taken calculus.
TheSomeone
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Ikerous said:
Oh well, i tried...
How does that have finite volume? Wouldn't the height of the shape be infinity?
dream431ca
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It's fun that I participated in this crazy thread..but you know what...the Someone is right. 0.999 does equal 1...I wanted to see if anyone could prove it...they didn't but I can...read and learn people:
The first thing to realize about the system of notation that we use (decimal notation) is that things like the number 357.9 really mean "3*100 + 5*10 + 7*1 + 9/10". So whenever you write a number in decimal notation and it has more than one digit, you're really implying a sum.
So in modern mathematics, the string of symbols 0.9999... = 1 is understood to mean "the infinite sum 9/10 + 9/100 + 9/1000 + ...". This in turn is shorthand for "the limit of the sequence of numbers
9/10,
9/10 + 9/100,
9/10 + 9/100 + 9/1000,
...."
One can show that this limit is 9/10 + 9/100 + 9/1000 ... using Analysis, and a proof really isn't all that hard (we all believe it intuitively anyway); a reference can be found in any of the Analysis texts referenced at the end of this message. Then all we have left to do is show that this sum really does equal 1:
Proof: 0.9999... = Sum 9/10^n
(n=1 -> Infinity)
= lim sum 9/10^n
(m -> Infinity) (n=1 -> m)
= lim .9(1-10^-(m+1))/(1-1/10)
(m -> Infinity)
= lim .9(1-10^-(m+1))/(9/10)
(m -> Infinity)
= .9/(9/10)
= 1
Not formal enough? In that case you need to go back to the construction of the number system. After you have constructed the reals (Cauchy sequences are well suited for this case, see [Shapiro75]), you can indeed verify that the preceding proof correctly shows
lim_(m --> oo) sum_(n = 1)^m (9)/(10^n) = 1
0.9999... = 1
Thus x = 0.9999...
10x = 9.9999...
10x - x = 9.9999... - 0.9999...
9x = 9
x = 1.
Another informal argument is to notice that all periodic numbers such as 0.9999... = 9/9 = 1 are equal to the digits in the period divided by as many nines as there are in the period. Applying the same argument to 0.46464646... gives us = 46/99.
Happy Now??
The first thing to realize about the system of notation that we use (decimal notation) is that things like the number 357.9 really mean "3*100 + 5*10 + 7*1 + 9/10". So whenever you write a number in decimal notation and it has more than one digit, you're really implying a sum.
So in modern mathematics, the string of symbols 0.9999... = 1 is understood to mean "the infinite sum 9/10 + 9/100 + 9/1000 + ...". This in turn is shorthand for "the limit of the sequence of numbers
9/10,
9/10 + 9/100,
9/10 + 9/100 + 9/1000,
...."
One can show that this limit is 9/10 + 9/100 + 9/1000 ... using Analysis, and a proof really isn't all that hard (we all believe it intuitively anyway); a reference can be found in any of the Analysis texts referenced at the end of this message. Then all we have left to do is show that this sum really does equal 1:
Proof: 0.9999... = Sum 9/10^n
(n=1 -> Infinity)
= lim sum 9/10^n
(m -> Infinity) (n=1 -> m)
= lim .9(1-10^-(m+1))/(1-1/10)
(m -> Infinity)
= lim .9(1-10^-(m+1))/(9/10)
(m -> Infinity)
= .9/(9/10)
= 1
Not formal enough? In that case you need to go back to the construction of the number system. After you have constructed the reals (Cauchy sequences are well suited for this case, see [Shapiro75]), you can indeed verify that the preceding proof correctly shows
lim_(m --> oo) sum_(n = 1)^m (9)/(10^n) = 1
0.9999... = 1
Thus x = 0.9999...
10x = 9.9999...
10x - x = 9.9999... - 0.9999...
9x = 9
x = 1.
Another informal argument is to notice that all periodic numbers such as 0.9999... = 9/9 = 1 are equal to the digits in the period divided by as many nines as there are in the period. Applying the same argument to 0.46464646... gives us = 46/99.
Happy Now??
spookymooky
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Is that area really finite? I cant picture that at all. Cool, though.Ikerous said:
TheSomeone, PLEASE stop with the double posts. If you have two things to say, just use one post.
TheSomeone
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dream431ca said:
Someone play some emotional violins, please.
dream431ca
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Ikerous said:
Please show me....I think not.
Proof: 0.9999... = Sum 9/10^n
(n=1 -> Infinity)
= lim sum 9/10^n
(m -> Infinity) (n=1 -> m)
= lim .9(1-10^-(m+1))/(1-1/10)
(m -> Infinity)
= lim .9(1-10^-(m+1))/(9/10)
(m -> Infinity)
= .9/(9/10)
= 1
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dream431ca
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Pesmerga said:
ktimekiller
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So... whats your point? e-peen boast?
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