Hi,

Many thanks in advance if you could help answering the following questions:

Q1 - Is M(e) > M(pi) true in the real numbers?

Q2 - Is the first order formal system T = ZFC + { M(e) > M(pi) } consistent?

(Where e and pi are the 2 familiar transcendental real numbers).

=========================> Definitions.

Let a real number x be generally expressed as:

I.d1d2d3...dn...

Where 'I' is the integral part and each 'dn' is a decimal expansion digit. Consider the sequence Sn defined as:

S1 = .d1d2d3...dn...

S2 = .d2d3...dn...

...

Sn = .dn(dn+1)(dn+2)...

...

Let's define M(x) ["Major number" of x] and m(x) ["minor" number of x] as:

M(x) = l.u.b (Sn)

m(x) = g.l.b (Sn)

Thanks,

-Nam Nguyen