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Author Topic: 1 = 2 ??? (I can prove it..)  (Read 2992 times)

Offline Seany

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1 = 2 ??? (I can prove it..)
« on: 25/04/2007 22:50:43 »
You may have seen this little proof that 2=1:

a = x `````````````[true for some a's and x's]
a+a = a+x `````````[add a to both sides]
2a = a+x ``````````[a+a = 2a]
2a-2x = a+x-2x ````[subtract 2x from both sides]
2(a-x) = a+x-2x ```[2a-2x = 2(a-x)]
2(a-x) = a-x ``````[x-2x = -x]
2 = 1````````````` [divide both sides by a-x]

YES.. OK, there are many mistakes between the steps. But it's still pretty cool! ;)


 

Offline Batroost

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1 = 2 ??? (I can prove it..)
« Reply #1 on: 25/04/2007 22:52:50 »
And the trick is that you are dividing by (a-x) which must equal zero as you've defined a as equal to x.

If you include a division by zero you can 'prove' anything!

Good trick though - must remember to try this on the kids....
 

Offline Seany

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1 = 2 ??? (I can prove it..)
« Reply #2 on: 25/04/2007 22:55:12 »
Yep. That's the hole in it. Dividing by 0 gives infinityyyyyyy... and beyond ;)
« Last Edit: 25/04/2007 23:37:41 by Seany »
 

another_someone

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1 = 2 ??? (I can prove it..)
« Reply #3 on: 25/04/2007 23:36:03 »
Yep. That's the whole in it. Dividing by 0 gives infinityyyyyyy... and beyond ;)

Except, you cannot get beyond infinity, but there are many different infinities, and some infinities are bigger than other infinities.
 

Offline Ben6789

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1 = 2 ??? (I can prove it..)
« Reply #4 on: 26/04/2007 13:16:53 »
what?
 

another_someone

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1 = 2 ??? (I can prove it..)
« Reply #5 on: 26/04/2007 14:06:20 »
http://en.wikipedia.org/wiki/Cardinal_number
Quote
In mathematics, cardinal numbers, or cardinals for short, are a generalized kind of number used to denote the size of a set. While for finite sets the size is given by a natural number - the number of elements - cardinal numbers (cardinality) can also classify degrees of infinity. On one hand, a proper subset A of an infinite set S may have the same cardinality as S. On the other hand, perhaps also counterintuitively, not all infinite objects are of the same size. There is a formal characterization of how some infinite objects are strictly smaller than other infinite objects.
 

Offline Ben6789

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1 = 2 ??? (I can prove it..)
« Reply #6 on: 26/04/2007 15:42:08 »
still don't understand
 

another_someone

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1 = 2 ??? (I can prove it..)
« Reply #7 on: 26/04/2007 16:04:21 »
OK, first you have to understand that in some way we are talking about two different things.  Number come in two forms, cardinal numbers and ordinal numbers.

The ordinal number deal with value and the order of number, whereas cardinality deals with the size of groups of things.  If you have a set of 3 number, the number are 5, 7, and 13.  The ordinality of the largest number is 13, but the cardinality of the set is only 3, because there are only 3 things in it.

Now look at how many numbers exist.  If one looks at the cardinality of the set of integers, there are infinite integers.  Some people might say that if you only look at the odd integers, even though all the integers are both odd and even integers, thus the number of even integer should be less than the number all integers, but in fact, you can show that for every integer there is an even integer that is twice the integer (i.e. Y=2X, where X is an integer, and Y is an even integer, so the set of Ys must be the same size as the set of Xs), so there must be an equal number of integers and even integers.

But now look at the number of real numbers that exist.  If one looks at the carnality (size of) the set of integers between 3 and 5, there are three integers, but how many real numbers exist in that set.  Even between 0 and 1, there are an infinite number of real numbers.  So if one looks at the number of real numbers between all of the infinite number of integer numbers, you find that you have a set which is an infinite times an infinite set.
 

Offline Ben6789

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1 = 2 ??? (I can prove it..)
« Reply #8 on: 26/04/2007 16:07:01 »
i see now..
 

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1 = 2 ??? (I can prove it..)
« Reply #8 on: 26/04/2007 16:07:01 »

 

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