- #1

CollinsArg

- 51

- 2

My statement is that: Irrational numbers are not infinite number, but numbers that can not be measured and that we have only found infinite aporoximate numbers to real irrational numbers.

For example: The number 1.41421... is not √2 but an infinite aproximation of √2.

Using the pythagoras theorem we can get to √2 by trying to know the measurement of the hypotenuse of a right triangle whose legs are 1cm each.

*x*^{2}+y^{2}*=*

*z*^{2}**=**

*1*^{2}+1^{2}

*z*^{2}*=*

**2**

**z**^{2}*=*

**√2**

**z**then the square of the hypotenuse is equal of 2, but when you try to find one of its sides, you realize that (trying to approach the number which multiplied by itself is equal of 2 ):

1.4

^{2}= 1.96 (aproximate n, but not 2) so you try 1.5

^{2}= 2.25 the number is bigger so we try to add decimals, then 1.41

^{2}= 1.9881 so you try 1.42

^{2}= 2.0164. So, you will keep trying adding decimals and you'll realize that you always get to an approximate number or a bigger number than 2, this way you create a number with infinite decimals which never get to approach the goal (multiplied by itself it's 2). Therefore 1.4121... is not exactly √2 but an infinite approximation to that number, therefore it is √2 immeasureble. And therefore 3.14... is neither π but an infinite aproximation of π. So irrational numbers can't be expressed in numbers. Am I right?

(English is not my first language, sorry if I made grammar mistakes).