### Math question: How to decide about rational and irrational numbers

Posted:

**Sat Mar 03, 2018 3:48 pm**Hi,

WARNING!

I am no math guru...by far not. The opposite is true...

As far as I had understood...

An integer number is a number, which has only '0's as fractional part...which is identical to "no fractional part at all".

A rational number is number, which can be expressed as a quotient from two integer numbers.

An irrational number is a number which is no integer number and no rational number and no complex number.

There are rational numbers, which fractional part stops at some point. For example 1 4 / 0.25

There are rational and irrational numbers, which fractional part doesn't stop but is repetive. For example 1 3 / 0.3333333333.....

Every fractional part, which is non-repetive and does not stop is part of a irrational number.

But:

Is there any mathematical proof, that the fractional part of a rational number is repetive or none-repetive or whether it stops or not?

Is this property an effect of the underlaying number system (decimal, etc) only?

For example:

How do we know, that PI is irrational...that is: The fractional part non-repetive?

It may be that afte the 9e9999999999999999999999999999999999999999999999999999999999999999999999 digit the fractional

part DOES repeat itsself....

(pi isn't a good example...but...)

I fear, that a brute-force attack to this problem with my DM42 will only empty the batteries...

Thanks a lot for any enlightment!

Cheers

Meino

WARNING!

I am no math guru...by far not. The opposite is true...

As far as I had understood...

An integer number is a number, which has only '0's as fractional part...which is identical to "no fractional part at all".

A rational number is number, which can be expressed as a quotient from two integer numbers.

An irrational number is a number which is no integer number and no rational number and no complex number.

There are rational numbers, which fractional part stops at some point. For example 1 4 / 0.25

There are rational and irrational numbers, which fractional part doesn't stop but is repetive. For example 1 3 / 0.3333333333.....

Every fractional part, which is non-repetive and does not stop is part of a irrational number.

But:

Is there any mathematical proof, that the fractional part of a rational number is repetive or none-repetive or whether it stops or not?

Is this property an effect of the underlaying number system (decimal, etc) only?

For example:

How do we know, that PI is irrational...that is: The fractional part non-repetive?

It may be that afte the 9e9999999999999999999999999999999999999999999999999999999999999999999999 digit the fractional

part DOES repeat itsself....

(pi isn't a good example...but...)

I fear, that a brute-force attack to this problem with my DM42 will only empty the batteries...

Thanks a lot for any enlightment!

Cheers

Meino