Factoring Real Numbers

r

4

4 =

2. × 2.

=

2. + 2.

Given any positive real number

r

, there exist some positive real numbers

r

1

,

r

2

, …,

r

n

, all less than 4, with

r=

r

1

r

2

…

r

n

and

r=

r

1

+

r

2

+…+

r

n

and also

r

2

r

3…

r

n

=

r

2

+

r

3

…+

r

n

,

r

3

r

4

…

r

n

=

r

3

+

r

4

+…+

r

n

, and so on. This factorization is unique. This Demonstration shows the factorization of numbers from 4 to 50, showing up to three decimals of the factors.