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#1 2006-11-29 10:35:31

luca-deltodesco
Member
Registered: 2006-05-05
Posts: 1,470

proof √2 is irrational

anyone see any errors in this?

is meant to doesn't divide, since \nmid doesnt work here










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#2 2006-11-29 11:26:36

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: proof √2 is irrational

The proof is valid.  However, why did you write the entire thing in symbol notation?  It is a lot easier to read and write if it's written out in words.  Typically, formal proofs are not written with any symbols.

There is one typo I believe:

Should be:

Same thing with the second to last line.


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#3 2006-11-29 20:13:00

luca-deltodesco
Member
Registered: 2006-05-05
Posts: 1,470

Re: proof √2 is irrational

no, i was right with the primes.

because otherwise that statment would mean that there are no rational numbers according to the proposition, because 1 is a member of the integers, and 0.5 can be written 1/2, and if you say integers, then both of them can be divided by an integer, so the proposition would be false?

And i just like symbols tongue


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#4 2006-11-30 00:04:30

Toast
Real Member
Registered: 2006-10-08
Posts: 1,321

Re: proof √2 is irrational

luca-deltodesco wrote:

anyone see any errors in this?

is meant to doesn't divide, since \nmid doesnt work here









faint

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#5 2006-11-30 05:24:20

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: proof √2 is irrational

luca-deltodesco wrote:

no, i was right with the primes.

because otherwise that statment would mean that there are no rational numbers according to the proposition, because 1 is a member of the integers, and 0.5 can be written 1/2, and if you say integers, then both of them can be divided by an integer, so the proposition would be false?

And i just like symbols tongue

Ok, so you meant primes.  I would be right if it was:


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#6 2006-12-27 22:04:50

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,905

Re: proof √2 is irrational

It basically means that if √2 is a rational, than there exist integers a,b, (a,b)=1, such that a^2=2b^2, so 2/a^2, but 2 is prime, so 4/a^2. But then 2/b^2, so 2/b, and we ,have 2/a and 2/b ,so (a,b)>=2, which is contradiction.


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