Fun with Infinity

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MAL

Approximation
« Reply #60 on: May 16, 2006, 12:56:01 PM »
It can be considered an approximation if you assume that 1/3 = 0,33333333333333333333333333333333333333333333333333333, and put as many decimals there as you like.  However, is you assume that 1/3 = 0,3... to the infinity, that is, with an infinite number of decimals, you can prove, exactly, that 0,999... recurring is indeed 1.

Fun with Infinity
« Reply #61 on: May 16, 2006, 01:05:05 PM »
I would have thought 0.9 recurring would = 0.9 recurring.

Just a thought.

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Erasmus

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Fun with Infinity
« Reply #62 on: May 16, 2006, 04:38:51 PM »
Quote from: "MiniCooper"
I would have thought 0.9 recurring would = 0.9 recurring.

Just a thought.


Yes, it is the case that any number is equal to itself.

It also happens to be the case that when you write any number in decimal notation, you are expressing it as a sum of multiples of powers of ten.  So if somebody proves that the sum represented by a given decimal string is equal to 1, then the number represented by that decimal string is equal to 1.

-Erasmus
Why did the chicken cross the Möbius strip?

Fun with Infinity
« Reply #63 on: May 16, 2006, 06:28:54 PM »
Quote from: "Erasmus"
Quote from: "MiniCooper"
I would have thought 0.9 recurring would = 0.9 recurring.

Just a thought.


Yes, it is the case that any number is equal to itself.

It also happens to be the case that when you write any number in decimal notation, you are expressing it as a sum of multiples of powers of ten.  So if somebody proves that the sum represented by a given decimal string is equal to 1, then the number represented by that decimal string is equal to 1.

-Erasmus


So I was right.

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Erasmus

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Fun with Infinity
« Reply #64 on: May 16, 2006, 08:06:37 PM »
Quote from: "MiniCooper"
So I was right.


You were right, but you were stating a tautology; you weren't saying anything at all.

-Erasmus
Why did the chicken cross the Möbius strip?

Fun with Infinity
« Reply #65 on: May 25, 2006, 08:49:35 AM »
Hmm, what is 0/0 ?

Everything divided by itself becomes 1, said my math teacher.

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Erasmus

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Fun with Infinity
« Reply #66 on: May 25, 2006, 12:07:58 PM »
Quote from: "Mattias_Olsson"
Hmm, what is 0/0 ?

Everything divided by itself becomes 1, said my math teacher.


Your math teacher is leaving out the fact that this only applies to things that can be divided by themselves.  Really, he/she means "Everything divisible by itself, when divided by itself, is 1."

0/0 is not defined naturally, but we can define it as a limit of some function, such as 0/x or x/x, as x approaches 0.  The limit of the first function is 0, whereas the limit of the second function is 1 (by l'Hopital's rule, if you care).

-Erasmus
Why did the chicken cross the Möbius strip?

Fun with Infinity
« Reply #67 on: May 25, 2006, 09:08:05 PM »
Quote from: "tigerhawkvok"
Quote
sphere fans seem to think all items of mass are drawn to eachother, but cannot explain why. Newton and Einstein couldn'

Incorrect.  Newton couldn't, Einstein could (distortions in the four-dimensional spacetime, a geometry effect).

Quote
0.9 recurring = 1.

Prove me wrong. I dares ya.


Let
X=.11111...
10X = 1.111111111....
Therefore,
10X-X=1
9X=1

However, since we defined X to be .111.....

9X=.99999999....

;-)


so wait, if I propose this question in fractions format, what do I get? (purely for testing purposes)

[yes, I did just read through the full thread if you're wondering. I just went back from the start because I remember this being mentioned on the first page and wanted to quote it without having a hassle.]

Let

x = 1/9

10x = 10/9
Therefore, 10x-x = 9x, alternately, 9/9
and 9/9 = 1

However, since we defined X to be 1/9,

9x = 9/9

Eeh, it isn't as cool in fractions XD

I do have a question though, but not infinity-related



We have 3 people who rent a room for one day.

It costs $30/day. So, each of the 3 people pay $10, equally.

Accidentally, the receptionist charged them the wrong price, as they were ordering a different type of room.  The actual price was $25/day.

So, the bellboy comes up and refunds them their $5. From their kindness, they let him keep $2.

Now, each of the 3 people have paid $9 instead of the $10 originally, and the bellboy has $2.

But 9x3+2 =/= 30.

...The fuck?

:)


I know I proved this wrong somewhere, but I'll let someone else do it this time :) There's a flaw of math somewhere in there, but I'm too lazy to find it right now.
RE*
Try not to be -too- much of an idiot. Or I'll rape you verbally.

1 out of 9 members on this forum that can spell properly.

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Escherichia

Fun with Infinity
« Reply #68 on: May 26, 2006, 01:12:57 PM »
Each of the guests paid (10-1=9) $. So altogether, they paid 27 $, which they distributed among the receptionist (25 $) and the bellboy (2 $).

Summing up what the guests have paid and what the bellboy has received just doesn't make sense.

Fun with Infinity
« Reply #69 on: May 26, 2006, 01:51:52 PM »
Yes, it does.

They paid 30 dollars to start with.

They got refunded 5.

Since they couldn't split that 5 equally, they gave 2 back to the bellboy.

That means they each got refunded 1 dollar (3 in total), and 2 went to the bellboy

Therefore, instead of paying 10 dollars each, they now paid 9 dollars, as each of them got refunded one.

Still following me?

9 x 3 = 27.

Add what the bellboy recieved, and you get 29.

So where'd that extra dollar go?
RE*
Try not to be -too- much of an idiot. Or I'll rape you verbally.

1 out of 9 members on this forum that can spell properly.

Fun with Infinity
« Reply #70 on: May 26, 2006, 01:53:18 PM »
to jupiter!

Fun with Infinity
« Reply #71 on: May 26, 2006, 04:33:03 PM »
You see? It just doesn't freaking add up.
RE*
Try not to be -too- much of an idiot. Or I'll rape you verbally.

1 out of 9 members on this forum that can spell properly.

?

Erasmus

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Fun with Infinity
« Reply #72 on: May 26, 2006, 06:35:41 PM »
Quote from: "mattz1010"
You see? It just doesn't freaking add up.


It doesn't add up because you can't just add random numbers together and expect it to make sense.  If however you are a rational person then:

Code: [Select]
Initially: Guests have $30, hotel has $0, bellboy has $0.

   event   |   guests now have   |   hotel now has  |   bellboy now has   | total
-----------+---------------------+------------------+---------------------+-------
 $30 room  |         $0          |       $30        |          $0         |  $30
 $5 refund |         $5          |       $25        |          $0         |  $30
 $2 tip    |         $3          |       $25        |          $2         |  $30



The total is always $30.  No money is "lost".

If you keep track of where the money is in a non-confusing way, it makes perfect sense.

-Erasmus

*edit* p.s. how is this "on the topic of infinity"?
Why did the chicken cross the Möbius strip?

Fun with Infinity
« Reply #73 on: May 27, 2006, 12:10:28 AM »
Quote from: "Myself, Me, and I"
I do have a question though, but not infinity-related


Yup, that's how.

Sorry 'bout that.

And thanks for reminding me, it was the manipulation of language and mathematics that made it equal to 29 dollars instead of 30.

[I'duse the dollar sign key,but alas, the spacebar, r, x, three, four, six, esc, f3, and f5 keys don't work. Numpad does, though.]
RE*
Try not to be -too- much of an idiot. Or I'll rape you verbally.

1 out of 9 members on this forum that can spell properly.

?

Erasmus

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Fun with Infinity
« Reply #74 on: May 27, 2006, 08:57:08 AM »
Quote from: "mattz1010"
Quote from: "Myself, Me, and I"
I do have a question though, but not infinity-related


Yup, that's how.

Sorry 'bout that.


Ah, my bad.... my memory/eyesight/ability to make informed judgements is deterioriating in my old age.

-Erasmus
Why did the chicken cross the Möbius strip?

Fun with Infinity
« Reply #75 on: June 01, 2006, 09:45:16 PM »
Ah, I figured it out, with the help of the graph.

It confuses you because it uses the uselessness of the english language to tell you that their 'money' is only equal to 27, when in fact, it is 28 (because 25 is in the cash machine)

:)
RE*
Try not to be -too- much of an idiot. Or I'll rape you verbally.

1 out of 9 members on this forum that can spell properly.

Fun with Infinity
« Reply #76 on: June 06, 2006, 08:26:27 AM »
Quote from: "humanbean"
According to the bible  1 man and 1 woman equals 1.
Soooooooooooooooo  1+1 can = 1

hehehehehe


actually... since the child is a PRODUCT of the parents, it is 1*1 = 1

Fun with Infinity
« Reply #77 on: June 06, 2006, 08:39:34 AM »
Quote from: "mattz1010"
Yes, it does.

They paid 30 dollars to start with.

They got refunded 5.

Since they couldn't split that 5 equally, they gave 2 back to the bellboy.

That means they each got refunded 1 dollar (3 in total), and 2 went to the bellboy

Therefore, instead of paying 10 dollars each, they now paid 9 dollars, as each of them got refunded one.

Still following me?

9 x 3 = 27.

Add what the bellboy recieved, and you get 29.

So where'd that extra dollar go?


no, you add what they have left to the 27.... what the bellboy got comes out of the $9 they paid

ie 25/3 for the room, 2/3 for the bellboy... each

Fun with Infinity
« Reply #78 on: June 23, 2006, 12:19:56 PM »
I would like to point out that math is not necesarily always correct

let a+b=c
so (4a-3a)+(4b-3b)=(4c-3c)  redefining 1
4a+4b-4c=3a+3b-3c
4(a+b-c)=3(a+b-c)
4=3
he man in black fled across the desert, and the gunslinger followed.

Advocatus Diaboli

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joffenz

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Fun with Infinity
« Reply #79 on: June 23, 2006, 01:21:29 PM »
Quote from: "CrimsonKing"
I would like to point out that math is not necesarily always correct

let a+b=c
so (4a-3a)+(4b-3b)=(4c-3c)  redefining 1
4a+4b-4c=3a+3b-3c
4(a+b-c)=3(a+b-c)
4=3


Not quite, because (a+b-c) =0

let a+b=c
so (4a-3a)+(4b-3b)=(4c-3c)  redefining 1
4a+4b-4c=3a+3b-3c
4(a+b-c) = 3(a+b-c)
4(c-c) = 3(c-c)    substitute c for (a+b)
4(0) = 3(0)
0 = 0

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Erasmus

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Fun with Infinity
« Reply #80 on: June 23, 2006, 01:48:27 PM »
Quote from: "cheesejoff"
Not quite, because (a+b-c) =0


Indeed.  Since, as cheesejoff points out, a+b-c = 0, the equation "x (a + b - c) = y (a + b - c)" is true for all values of x and y.
Why did the chicken cross the Möbius strip?

Fun with Infinity
« Reply #81 on: June 24, 2006, 04:39:52 PM »
Oh well if youre gonna do the math right, than you cant have nearly as much fun with the numbers.  Yes i realize its flawed, but it is quite fun to mess with people with, as usually they cannot find the flaw :D
he man in black fled across the desert, and the gunslinger followed.

Advocatus Diaboli

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Erasmus

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Fun with Infinity
« Reply #82 on: June 24, 2006, 04:44:18 PM »
Quote from: "CrimsonKing"
... but it is quite fun to mess with people with, as usually they cannot find the flaw :D


Not as much fun as understanding what the flaw is, I claim.
Why did the chicken cross the Möbius strip?