Author Topic: I'm more or less horrible at mathematics/symbolic logic...  (Read 4204 times)

Offline The Spy

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Re: I'm more or less horrible at mathematics/symbolic logic...
« Reply #25 on: June 07, 2009, 01:31:55 PM »
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At the expense of butchering the theory behind the equation, I would solve it by looking at the original form. Infinity/Infinity is considered an indeterminant and you have to multiply the equation by 1/Infinity/1/Infinity to get your answer. That is all I can say. My math might be a little rusty, but I think that if you used that situation, the variables X and Y would not enter your equation.
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Offline Egyptian

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Re: I'm more or less horrible at mathematics/symbolic logic...
« Reply #26 on: June 07, 2009, 01:52:21 PM »
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Hey,

Infinity x X or Y is still infinity. I'd say that's an equality.

Even when fudging the math and considering the idea of infinity in equations, the equation "infinity = infinity" is not always true.  There are different orders of infinity that are not "equal" to each other.  The way it was explained to me was that if hotel A has one floor and an infinite number of rooms on each floor and hotel B has an infinite number of floors and an infinite number of rooms on each floor then both hotels have an infinite number of rooms but hotel B has far more rooms than hotel A.

Tschow,

Tim "Sir Nobody" Maly

I think what you're trying to get at here is "countably infinite" versus "uncountably infinite."

A set is finite if and and only if its elements can be mapped to {1, 2, 3, 4,...X} where X > 0 and is an integer.
A set is countably infinite if and if only if its elements can be mapped to the set I = {1, 2, 3, 4,...}
If a set is neither countably infinite nor finite, then it is uncountably infinite.

In your example here, even if hotel B contained an infinite number of floors with an infinite number of rooms, it is still "only" countably infinite because I can map each floor to the set {1,2,3,...} and on each floor, I can map each room to the set {1,2,3,4...}. The union of two countably infinite sets is still countably infinite. In the vernacular, there is no mathematical difference between hotel A and hotel B.

An example of an uncountably infinite set is the set of real numbers R=[0,1]. If you try to set up a correspondence to the set {1,2,3,...} say by letting x2 >x1, x1 in [0,1] -> 1, x2 in [0,1] -> 2, etc., then to what element in I does (x1+x2)/2 correspond? This is the problem. No matter how small the difference between x2 and x1, you can always find an element (x1+x2)/2 that will not be able to be mapped to an element in I. You can always "squeeze another number in." Since the set is clearly not finite, and a one-to-one mapping between R and I cannot be established, R is uncountably infinite.

Another example of an uncountably infinite set is the Cantor set, K. This is obtained by deleting the middle third (1/3, 2/3) from [0,1]. Then, you delete the middle third from the segments [0,1/3) and (2/3,1]. Repeat this process ad infinitum, and the dust of points that remain is K. K is uncountably infinite for reasons that are beyond the scope of this post. :-)

-Egyptian
« Last Edit: June 07, 2009, 01:57:13 PM by Egyptian »
Those who are merciful to the cruel will, in the end, be cruel to them that deserve mercy. -Midrash

Offline YourMathTeacher

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Re: I'm more or less horrible at mathematics/symbolic logic...
« Reply #27 on: June 07, 2009, 02:01:26 PM »
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Another example of an uncountably infinite set is the Cantor set, K. This is obtained by deleting the middle third (1/3, 2/3) from [0,1]. Then, you delete the middle third from the segments [0,1/3) and (2/3,1]. Repeat this process ad infinitum, and the dust of points that remain is K. K is uncountably infinite for reasons that are beyond the scope of this post. :-)

This is Chaos!   :o
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Offline Egyptian

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Re: I'm more or less horrible at mathematics/symbolic logic...
« Reply #28 on: June 07, 2009, 02:06:57 PM »
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Another example of an uncountably infinite set is the Cantor set, K. This is obtained by deleting the middle third (1/3, 2/3) from [0,1]. Then, you delete the middle third from the segments [0,1/3) and (2/3,1]. Repeat this process ad infinitum, and the dust of points that remain is K. K is uncountably infinite for reasons that are beyond the scope of this post. :-)

This is Chaos!   :o

What I love about K is that it "seems" infinitely "less" than [0,1] yet is itself uncountably infinite!
Those who are merciful to the cruel will, in the end, be cruel to them that deserve mercy. -Midrash

Offline YourMathTeacher

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Re: I'm more or less horrible at mathematics/symbolic logic...
« Reply #29 on: June 07, 2009, 02:12:04 PM »
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What I love about K is that it "seems" infinitely "less" than [0,1] yet is itself uncountably infinite!

Unfortunately my students don't share the love when I make them draw the first 5 iterations of the Cantor Set. However, they do enjoy the Koch Snowflake since it is the only snow they get here in Florida.  ;D
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Offline SirNobody

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Re: I'm more or less horrible at mathematics/symbolic logic...
« Reply #30 on: June 07, 2009, 03:02:56 PM »
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Hey,

I think what you're trying to get at here is "countably infinite" versus "uncountably infinite."

Right!  That...wow my math is rusty.  The uncountability of the real numbers never sat well with me.

Tschow,

Tim "Sir Nobody" Maly

Offline Colin Michael

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Re: I'm more or less horrible at mathematics/symbolic logic...
« Reply #31 on: June 07, 2009, 03:19:47 PM »
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So yeah, I'm an autodidact: all I know about math is self taught.

I'm kind of confused and lost with all of this.

αθαvαTOι θvηTOι θvηTOι αθαvαTOι ζwvTεs TOv εKειvwv θαvαTov Tov δε εKεivwv βιOv TεθvεwTεs -Heraclitus

Offline YourMathTeacher

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Re: I'm more or less horrible at mathematics/symbolic logic...
« Reply #32 on: June 07, 2009, 03:25:10 PM »
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I'm kind of confused and lost with all of this.

You're confused by big numbers and I'm confused by big words. I say we're even.  ;D
« Last Edit: June 07, 2009, 03:32:10 PM by YourMathTeacher »
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Offline Colin Michael

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Re: I'm more or less horrible at mathematics/symbolic logic...
« Reply #33 on: June 07, 2009, 03:29:42 PM »
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I'm kind of confused and lost with all of this.

Your confused by big numbers and I'm confused by big words. I say we're even.  ;D
Touche.
αθαvαTOι θvηTOι θvηTOι αθαvαTOι ζwvTεs TOv εKειvwv θαvαTov Tov δε εKεivwv βιOv TεθvεwTεs -Heraclitus

Offline Egyptian

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Re: I'm more or less horrible at mathematics/symbolic logic...
« Reply #34 on: June 07, 2009, 09:36:41 PM »
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The uncountability of the real numbers never sat well with me.

There are support groups for that, you know. The first step is admitting you have a problem... LOL
Those who are merciful to the cruel will, in the end, be cruel to them that deserve mercy. -Midrash

Offline YourMathTeacher

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Re: I'm more or less horrible at mathematics/symbolic logic...
« Reply #35 on: June 07, 2009, 10:08:42 PM »
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... and the second step is to subtract the constant from both sides of the equation....
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