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Originally posted by PersianMafia Yeah, it's those far more complex things that the college boards actually bother to test you on... :runs off screaming thinking of his ap calc exam this may:

i will also be taking that test...


OMG TImE to STUDAY!!!

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1=1? How can one number be equal to another? I could never see that.

they are the same number..

1+1 = 2 2 of one thing. maybe thats how different combinations of numbers can equal the same thing.

DID YOU KNOW - .99999999999 = 1 it is equal to one. think about it. what is 3/3 in decimal form. 1/3 = .33333333 2/6 = .6666666666 3/3 = .999999999999 but we all know something like 3/3 or 5/5 = 1. so all .9999999 = 1

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Originally posted by ::TranceVanDyk:: we're doing quadratic equations in algebra 2 now. they suck but they're do'able.

HAHAHHA


quadratic... ah, kids

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Originally posted by ::TranceVanDyk:: they are the same number.. 1+1 = 2 2 of one thing. maybe thats how different combinations of numbers can equal the same thing. DID YOU KNOW - .99999999999 = 1 it is equal to one. think about it. what is 3/3 in decimal form. 1/3 = .33333333 2/6 = .6666666666 3/3 = .999999999999 but we all know something like 3/3 or 5/5 = 1. so all .9999999 = 1

That is incorrect, if you round it then yes, ".99999999999 = 1" but as it is, what you wrote is 99999999999/100000000000, which is in fact not equal to 1, but 1/100000000000 away from equaling 1.

First I will postulate that a number divided by the exact same number one time only will equal 1.

3/3 does in fact equal 1, because you have the exact same number in the numerator as you do in the denominator. The same goes for 5/5. However, in your example, your numerator is not exactly the same as your denominator, and is therefore not 1.

And for reference, 2/6 does not equal .6666666666. If you reduce the fraction, you will see that 2/6 is the same as 1/3, which is the repeating decimal .3

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Originally posted by Zenchowdah HAHAHHA quadratic... ah, kids

lol what an asshole

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Originally posted by Orbital32 i got a cool math trick: start/run/calc Wahlaaa!

OMG don't give away that secret!!

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Originally posted by Tranc3 And for reference, 2/6 does not equal .6666666666. If you reduce the fraction, you will see that 2/6 is the same as 1/3, which is the repeating decimal .3

that was a little mistake.

i meant 2/3 = .66666666666666666.

i will research and show u that .99999999 really does equal one. a mathematician showed me once and i will find out how u write it out.

Why does 0.9999... = 1 ?
This answer is adapted from an entry in the sci.math Frequently Asked Questions file, which is Copyright (c) 1994 Hans de Vreught ([email protected]).
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.

quote:

Originally posted by ::TranceVanDyk:: Why does 0.9999... = 1 ? This answer is adapted from an entry in the sci.math Frequently Asked Questions file, which is Copyright (c) 1994 Hans de Vreught ([email protected]). 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.

Well certainly, the limit as N approaches infinity of the sum(i) from i=1 to n will equal infinity....if it's, say, a 9 behind a decimal, then yes the repeating number does indicate that it approaches 1. However, the only correct way to interpret your notation would be with significant figures....that is, you were measuring out a number to the nth significant place (and therefore simply truncating the remainder, changing the value of the sum, as it no longer approached infinity but rather a finite number).

The formal argument makes perfect sense and is absolutely correct logically, but you didn't follow the conditions necessary for the argument to support your conclusion.

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Originally posted by Sunsnail I went over to a friend's house, and his mother teaches math.

go up to his mom and be like "i'm a math genious like you! You + Me - Clothes / your legs, and hope we don't multiply, biatch!!"

Anyone else here a math major? This is all fun stuff to me, or at least it should be since I'm probably gonna end up doing it for a living in a few years...

Being in 4th year of an Honours Physics Degree lets me tell you that yes, you all have a very long way to go yet It gets much, much harder.

Don't tell the three secrets of the number six! Number six and his bag of tricks. I'm in love with the number six, and the number six loves me. I had sex seven times with the number six in the shadow of a tree. Six has zero friends and one bastard child named nine. It's only twelve o'clock number six, don't run away this time!

My math prof this year was telling our class that most mathematicians throughout the ages that have attempted to analyze infinity and infinit limits have all gone insane as a result of their attempts.

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Originally posted by PersianMafia My math prof this year was telling our class that most mathematicians throughout the ages that have attempted to analyze infinity and infinit limits have all gone insane as a result of their attempts.

simply, we just cant comprehend infinite with our finite understanding. thus, what really is infinite? jesus called Himself, Alpha/Omega, beginning and end. God told moses, "I am that I am." could the christian god be the essence of infinite? or could it be brahman, or the cosmos? has the universe always been here? we just dont know...that is enough to drive a man insane.

quote:

Originally posted by Tranc3 Well certainly, the limit as N approaches infinity of the sum(i) from i=1 to n will equal infinity....if it's, say, a 9 behind a decimal, then yes the repeating number does indicate that it approaches 1. However, the only correct way to interpret your notation would be with significant figures....that is, you were measuring out a number to the nth significant place (and therefore simply truncating the remainder, changing the value of the sum, as it no longer approached infinity but rather a finite number). The formal argument makes perfect sense and is absolutely correct logically, but you didn't follow the conditions necessary for the argument to support your conclusion.

ok, all i know is that .99999 = 1 and i dont know how to explain it. so i got a source to do the explaining for me. u disagree, and im not as advanced in math as you, therefore i cant debate the subject with you. so i suggest u ask this dr. math guy and see what he says.

http://mathforum.org/dr.math/ask/

or simply ask your professor.

What the fuck is "math"

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Originally posted by ::TranceVanDyk:: ok, all i know is that .99999 = 1 and i dont know how to explain it. so i got a source to do the explaining for me. u disagree, and im not as advanced in math as you, therefore i cant debate the subject with you. so i suggest u ask this dr. math guy and see what he says. http://mathforum.org/dr.math/ask/ or simply ask your professor.

well...
_
.9 not .9999

quote:

Originally posted by Sunsnail well... _ .9 not .9999

same thing, just easier to type out.

quote:

Originally posted by Tranc3 Calc is based on Differentiation and Integration. The fundamental theorem of calculus involves taking the derivative of an integral, nothing more. Sure, their uses imply far more complex things, but calc is built off of those two principles.

Sorry but its simplier than that

Fundamental Theorem of calculus:

if f is continuous on [a,b] and if F is any integeral of f on [a,b] then
b
S f(x)dx = F(b) - F(a)
a

note: plain text sucks, the S a b is a integral defined between b and a.

quote:

Originally posted by ::TranceVanDyk:: ok, all i know is that .99999 = 1 and i dont know how to explain it. so i got a source to do the explaining for me. u disagree, and im not as advanced in math as you, therefore i cant debate the subject with you. so i suggest u ask this dr. math guy and see what he says. http://mathforum.org/dr.math/ask/ or simply ask your professor.

No, I agree completely with the paper you pasted. I disagree with you. .9999 (with an arbitrary but finite number of nines) is not the same as .9999 (with an infinite number of nines)

quote:

Originally posted by Dr. Cfire Sorry but its simplier than that Fundamental Theorem of calculus: if f is continuous on [a,b] and if F is any integeral of f on [a,b] then b S f(x)dx = F(b) - F(a) a note: plain text sucks, the S a b is a integral defined between b and a.

Well really if you think about it, it's even simpler than that. Differentiation and integration are both based on and couldn't exist without limits. Even though the actual fundamental theorem of calculus states (http://en.wikipedia.org/wiki/Fundam...rem_of_calculus), I feel the truly fundamental theorem of calculus is the epislon-delta definition of the limit. But I'm not a mathematician, so I'm not the most qualified to say that kind of thing.

quote:

Originally posted by ::TranceVanDyk:: same thing, just easier to type out.

One is impossible to type out, one is a finite value. Well both are actually finite values, in this case anyways, but the one that can be fully typed out without shorthand notation is not equal to 1.

Re: Cool math tricks!

quote:

Originally posted by Sunsnail Here are some neat math short-cuts that you can do in your head 142 213 +431 When you see a math problem like this, you were probably taught to add the right-most column first. Then the middle, then the left-most. But, doing it from left to right is actually much faster! Start with the left column. 1+2+4 is 7. Keep 700 in your mind. Then add the middle column. 740 -> 750 -> 780. Then the last column. 782 -> 785 -> 786 See how much faster and quicker that was? Here's another one: 346 473 +170 So, first add the left column. 8(00). Then the middle column. 180. Uh-oh, its more than 100. So add 100 to 800, and you're left with just 80. Now the last column: 989 is the final answer! Here's one with multiplication: 24 x12 Now, do the right column. 2x4=8. Now, cross multiply 4x1, and 2x2, and add the sum together. which is 8. Now multiply The left column, 2x1. Which is 2. The answer is 288. Pretty cool huh? Here are some more problems to practice with. Check them with a calculator to see if you're right. 63 x52 532 125 +842 32 x64

none of your methods made my calculations faster
took me 3-4 seconds each. either way

oh, and about math in general, i never studied it at school, i just showed up for the tests and learned most of what i was supposed to do from the tests themselves. (i got 100% on all the math tests that didnt include trig, except for a few times, when the teacher was a bitch and reduced my score for not showing how i got to my solution.... i always just wrote the answer, calculated all inside my head)

never managed trig though, the teacher always said im only one step away, but i couldnt be bothered to find out that extra step

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