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Unless they are not algebraically independent, e and pi,

then the form as follows

e/pi

Is the same as (for basic arithmetic purposes):

X/Y

In the rational functions Q(X,Y). See also

here, its very easy:

Tag 030D: 9.26. Transcendence

http://stacks.math.columbia.edu/tag/030D

Example 9.26.6. Consider the field extension Q(e,π)

formed by adjoining the numbers e and π. This field

extension has transcendence degree at least 1 since

both e and π are transcendental over the rationals.

However, this field extension might have transcendence

degree 2 if e and π are algebraically independent.

Whether or not this is true is unknown and whence

the problem of determining trdeg(Q(e,π)) is open.

The polynomials Q[X,Y], are just bivariate polynomials

with coefficients of Q and variables X,Y. The Q(X,Y)

is the field of fractions of Q[X,Y].

https://en.wikipedia.org/wiki/Field_of_fractions

To do more than basic arithmetic, you need F or C,

then Q(e,pi) is not enough. But +, -, *, / are

defined in a field of fractions,

What you need is a multivariate kind of division

and a multivariate GCD, which is a little tricky,

but Q[X,Y] is a GCD domain.

https://en.wikipedia.org/wiki/GCD_domain

I have implemented Q(X1,..,Xn) in Prolog, you

can play with it. Computing with E and PI, only

basic arithmetic, is very easy:

Jekejeke Prolog 2, Runtime Library 1.2.3

(c) 1985-2017, XLOG Technologies GmbH, Switzerland

?- use_module(library(groebner/generic)).

% 22 consults and 0 unloads in 938 ms.

Yes

?- X is (E^2-PI^2)/(E-PI).

X is E+PI

You can make a sanity check via approximations,

and using your pocket calculator (rounded and

with the usual float IEEE errors):

e^2-pi^2 = -2.4805483021587085

e-pi = -0.423310825130748

(e^2-pi^2)/(e-pi) = 5.859874482048839

e+pi = 5.859874482048838

Note this method (the result X is E+PI) of basic

arithemtic via polynomial factions works in finite

steps. You don't need infinity.

Can you refute that it works?

*Post by bassam king karzeddin**Post by bassam king karzeddin*Big Hint: remove both decimals notations from (e & pi) to estimate (e/pi) to avoid any confusions

Have more fun with the new resultant number for sure

Regards

Bassam King Karzeddin

May 25, 2017

So, what exactly is this genius mathematicians? wonder!

e/Pi = (2718281828...)/(3141592654...)

Forget about your APPROXIMATIONS, (we know it for sure)

Can't you think properly?

Or had you got addicted to fictions? wonder!

But I know that fictions are so sweet, but reality is much sweeter for sure

So, get out of your tiny hole and say a word of truth, now

Do something useful professional mathematicians for the societies that feed you, it is still not too late

But never feel shameful if you are so professional in mathematics since there is a lot that you had missed in the last few thousands of years, for sure

Regards

Bassam King Karzeddin

07/20/2017