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TheDeath
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with serious business
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posted January 15, 2010 09:49 PM |
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Edited by TheDeath at 21:51, 15 Jan 2010.
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I get what you're saying but I still find it unintuitive. And of course, I'm sorry for not being clear, but I meant that any infinite set with finite boundaries is the same as any other such set in cardinality.
I'm using this sort of "logic":
lim x->oo (2x/x) = 2  (making the (0,2) twice as big)
EDIT: oops actually it's not supposed to be x->oo but quantized infinitely. so ignore that but you get what I'm saying.
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ihor
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Accidental Hero
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posted January 16, 2010 08:37 PM |
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I don't get that sort of "logic".
What is relation between cardinality and those limits?
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TheDeath
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posted January 18, 2010 09:43 PM |
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Edited by TheDeath at 21:44, 18 Jan 2010.
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Well it's more closer to 1/x instead (when x goes to infinity) because you need to quantize it infinitesmally. The relation is that you can consider a 'continuous' range like a discrete (quantized) range, but with more and more resolution (infinitely so). Anyway it's probably because of my very discrete-thinking mind 
Either way, the resolution is cancelled and the (0,2) range is always larger than (0,1) exactly twice. (no matter the resolution)
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Mytical
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Chaos seeking Harmony
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posted January 20, 2010 07:22 AM |
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Edited by Mytical at 11:56, 20 Jan 2010.
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Ok this SHOULD be an easy problem but my mind has decided to freeze up on it...
Solving for Linear Inequalities, and have to graph the solution on a number line.
3x < 3(x-2)
So we take and multiply the second 3 by x and - 2...
3x < 3x - 6
Now here is where I get lost...
If I move the 3x over it is basically 0 < -6 right? Which is a false statement. So even if we flip the sign.. 0 > -6...how do I graph that on a number line? *is lost*..
If I take the 6 over..
3x + 6 < 3x
Doesn't really solve anything...
Even if we plug a number into x...
Say -2...
6 - 6 < -6
0 < -6
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winterfate
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posted January 20, 2010 07:32 AM |
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Ugh. Math.
Ok, let's see:
How about dividing by three on both sides, that gives you:
X < X - 6/3
By dividing you switch the sign, so it's actually
X > X - 2
Someone correct me if I'm wrong, my pre-Calc's a bit rusty (brain bleach to that part of my brain to forget the horrors of Math may have contributed. )
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If you supposedly care about someone, then don't push them out of your life. Acting like you're not doing it doesn't exempt you from what I just said. - Winterfate
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Mytical
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posted January 20, 2010 07:37 AM |
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Edited by Mytical at 07:37, 20 Jan 2010.
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Winter..even if accurate, doesn't help me on how to graph it on a number line. I am guessing that it will be x < or = -2 so..
<___]|_0_____>
-2
?
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winterfate
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posted January 20, 2010 07:40 AM |
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Lol, so rusty I forgot how to do that.
However, Wiki forgets nothing! 
http://www.wikihow.com/Graph-Inequalities
It jogged my memory a bit, so I think it's accurate. Try it out with your inequation and see what happens. 
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If you supposedly care about someone, then don't push them out of your life. Acting like you're not doing it doesn't exempt you from what I just said. - Winterfate
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Mytical
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posted January 20, 2010 08:10 AM |
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After working it out .. think the answer is no answer or 0 with a slash through it...
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winterfate
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posted January 20, 2010 08:38 AM |
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I'd think you're right.
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If you supposedly care about someone, then don't push them out of your life. Acting like you're not doing it doesn't exempt you from what I just said. - Winterfate
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Ecoris
Promising
Supreme Hero
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posted January 20, 2010 10:53 AM |
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Yes. No value of x satisfies 3x < 3(x-2).
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alcibiades
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of Gold Dragons
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posted January 20, 2010 11:55 AM |
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Quote:
Ok this SHOULD be an easy problem but my mind has decided to freeze up on it...
Solving for Linear Inequalities, and have to graph the solution on a number line.
3x < 3(x-2)
So we take and multiply the second 3 by x and - 2...
3x < 3x - 6
Now here is where I get lost...
If I move the 3x over it is basically 0 < -6 right? Which is a false statement. So even if we flip the sign.. 0 > -6...how do I graph that on a number line? *is lost*..
If I take the 6 over..
3x - 6 < 3x
Doesn't really solve anything...
Even if we plug a number into x...
Say -2...
-6 - 6 < -6
-12 < -6 is correct..but still don't have a clue how to graph it..
No, bolded part is wrong. If you take over 6, the correct equation reads:
3x + 6 < 3x
And hence: 6 < 0 which is still untrue for all x.
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What will happen now?
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Mytical
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Chaos seeking Harmony
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posted January 20, 2010 11:57 AM |
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Edited by Mytical at 11:58, 20 Jan 2010.
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I have no idea what you are talking about. *whistles innocently*
On a serious note, no wonder I couldn't solve it...gah. Shiny Things Syndrome stinks when trying to solve a math problem.
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alcibiades
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posted January 20, 2010 12:02 PM |
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Do you have to solve it graphically?
You can plot two lines, Y_1 = 3X and Y_2 = 3(X-2)
You will notice that these lines are parallel and that Y_1 lies above Y_2 (and does so for all X, since they are parallel).
Hence the statement Y_1 < Y_2 is untrue for all X.
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What will happen now?
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Mytical
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Chaos seeking Harmony
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posted January 20, 2010 12:06 PM |
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No, just on a straight number line. Which would be impossible. So the answer is just 0 with a slash through it.
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Ecoris
Promising
Supreme Hero
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posted January 20, 2010 04:05 PM |
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Yes, Ø, the empty set. (This is actually a proper Danish letter. I have such a key on my keyboard ).
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dimis
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posted January 25, 2010 04:02 PM |
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Hey guys,
It took me a while to be back and post. Anyway, regarding the solution of the
(0,1) =_c (0, 1]
problem. Here we go.
So, we have a problem with f(1) being 1 if we select f(x) = x for x in (0,1].
So, let's define it differently, say
f(1) = 1/2 and the rest of f as is.
Now the problem propagates on f(1/2) which 1/2. Ok.
Let's define f(1/2) = (1/2) * (1/2) = 1/4.
Now we have a problem with f(1/4), but we follow the same strategy.
We get rid of the problem though by "hiding" all those problems very close to 0 by successively working with powers of two.
So, let's define our f : (0,1] ---> (0,1)
f(x) = x/2, if x = 2^{-n} for some natural number non-negative integer n
f(x) = x, otherwise
Anyway, I hope you liked it.
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The empty set
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Mytical
Responsible
Undefeatable Hero
Chaos seeking Harmony
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posted February 09, 2010 09:22 AM |
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Two word problems..need to know formula and answer.
A recent owner of a cafe ordered 50lbs of coffee and 12lbs of tea for $354. The next order was for 30lbs of coffee and 6lbs of tea for 207. What is the cost per pound of each. Using the following statements.
Let x equal the cost per pound of Coffee
Let y equal the cost per pound of Tea
Second problem
Each question in section A was worth 4 points, and each question in section b was worth 8 points. Emily answered 13 questions correctly scoring 80 points. How many questions in section A did Emily answer correctly. Using the following Statements.
Let x = the number of questions correct in section A
Let y = the number of questions correct in section B
I know the answers are right in front of my face, but my brain has packed up and went off to vacation in Hawaii without me.
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Shares
Supreme Hero
I am. Thusly I am.
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posted February 09, 2010 10:13 AM |
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Edited by Shares at 19:37, 09 Feb 2010.
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Ok, so I did the first, but then my computer crashed, so I'll do the second one only. I know it looks long and complicated, but I'm just being thorough.
Second problem
Each question in section A was worth 4 points, and each question in section b was worth 8 points. Emily answered 13 questions correctly scoring 80 points. How many questions in section A did Emily answer correctly. Using the following Statements.
Let x = the number of questions correct in section A
Let y = the number of questions correct in section B
This means that x gives 4 points, y 8. X is the number of 4 points questions, y the 8 points one.
The first step is to write the "equation system"(is that what it's called in english), that is done by writing two separate equations.
4x+8y=80 These are the points, sums up to 80.
x+y=13 The number of questions, 13.
The second step is to make sure there's only ONE variable in ONE of the equations. So lets take the small one first.
x+y=13 reduce by y on both sides!
x=13-y Now you "know" x, so replace x in the other equation.
4x+8y=80 Should become;
4(13-y)=80 Remove the parantheses!
52-4y+8y=80 Count 8y-4y, and reduce by 52 on both sides!
4y=28 Divide by 4!
y=7 Now it's easy to get x! Go back to the other equation.
x=13-y y=7, now it's just obvious!
X=13-7
X=6
So the answer is:
X=6
Y=7
Or:
She answered 6 section A questions and 7 section B answers!
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ihor
Supreme Hero
Accidental Hero
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posted February 09, 2010 07:33 PM |
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The first:
50x + 12y = 354
30x + 6y = 207
The system of linear equalities.
Multiply second by 2:
50x + 12y = 354
60x + 12y = 414
Subtract:
10x = 60 -> x = 6
300 + 12y = 354 -> y = 54/12 = 4.5
Answer: x=6, y=4.5
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Mytical
Responsible
Undefeatable Hero
Chaos seeking Harmony
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posted February 10, 2010 09:31 AM |
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Edited by Mytical at 09:53, 10 Feb 2010.
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Ok now this one hehe. Promise it will be the last for awhile.
2x-y+z=1
3x+y+2z=-2
x-3y+2z=0
Got as far as...
2x-y+z=1
3x+y+2z=-2
=========
5x+3z=-1
I BELIEVE the next step would be..
3(2x+y+z)=1(3)
x-3y+2z=0
6x+3y+3z=3
x-3y+2z=0
===========
7x+5z=3
Then
I get lost. Did I choose the wrong next step? While I can eliminate either x or z .. it would get really complicated since I have to find a common denominator for either 5 and 7 or 3 and 5...
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