Pi and e Fully Defined from a Function - and Similar, Improper Fractions

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Q = [ rational numbers]

n ∈ N

Pi ∈ Q

Q = ( 4 * ( n + 1 ) + 3 ) / 7

f (x) = ( 4 * ( x + 1 ) + 3 ) / 7

x = 1 evolves the value 3 1/7 , 22/7 or Pi.

x = 3 evolves the value 19/7, the true ratio of e.

IT programming via iteration or estimation is what currently propagates the accepted Windows DOS, Pi value. The values above are not estimation. They are the true, accurate and precise values of Pi and e.

There is no such thing as an irrational number. When a rational, decimal fraction is inverted, a natural number is the result. Each rational number with a digital fraction string has an infinitely recurring number string. Those strings are usually within ten digits long, from the first significant figure. I invite any alternative observers to comment, on Spaces by Wix.

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