Re: PROVE sqrt(2)+sqrt(3) is a irrational number!!!

On Sun, 30 Sep 2007 18:10:29 -0700, ChineseBoy who loves maths
<h2oqu@xxxxxxxxxxxx> wrote:


You still need to prove:

1) a rational number times a irrational number is a irrational number.

Lets write <i> to denote "an irrational number" and <r> to denote "a
rational number".

Claim: <r> * <i> = <i>.

Proof: Assume <r> * <i> = <r>, then <i> = <r> / <r> = <r>.
Contradiction! []


2) a rational number plus a irrational number is a irrational number.

Claim: r + i = i.

Proof: Assume <r> + <i> = <r>, then <i> = <r> - <r> = <r>.
Contradiction! []


3) If a*a is irrational, then a is irrational.

Claim: a*a is <i> => a is <i>

Proof: Suppose a*a is <i>. Now assume a is <r>. Then a*a is <r> too.
Contradiction! []


F.

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