On Apr 29, 3:36 am, Graham Cooper <grahamcoop...@gmail.com> wrote: > On Apr 28, 3:58 am, Zuhair <zaljo...@gmail.com> wrote: > > > > > > > > > > > On Apr 27, 3:55 pm, Jan Burse <janbu...@fastmail.fm> wrote: > > > No > > > > Zuhair schrieb: > > > > > Pre-ZFC is a first order theory with the following axioms: > > > > > (1) Powerful Boundedness: if phi is a formula in which x,y are free, > > > > then > > > > all closures of: > > > > > EB: (Vy in B(Ex C A:phi)) & (Vx C A ((Ey:phi) ->(Ey in B:phi))) > > > > > are axioms. > > > > > C is subset relation. > > > > V;E signifies universal; existential quantification respectively. > > > > > 2) Infinity. > > > > > / > > > > > The whole of ZFC can be interpreted in Pre-ZFC. > > > > > Zuhair > > > Hmmm,... you must have figured out some flaw somewhere, what is it? > > > Zuhair > > B is any set in the world of mathematics! > > EB: (Vy in B(Ex C A:phi)) & (Vx C A ((Ey:phi) ->(Ey in B:phi))) > > is > > Exist B ALL y in B ... Exist X C A:phi > & > All X C A (Exist y:phi -> Exist y in B:phi ) > > *************** > > 1st line: > > yeB <-> SUBSET X OF A with elements that satisfy phi > > 3rd line: > > ALL subsets of A.. > y satisfies phi -> y e B (that satisfy phi) > > --------------- > > firstly, is the final phi in B:phi necessary > since phi already designates members of B > > secondly, All subsets of A is a POWERSET operation > on all SETS in the THEORY which has huge complexity > > thirdly, this is starting to look like mereology where > on starting equation is given to derive the rest.. > > the problem with mereology is it uses ALL(S) quantifier > and C (subset) to co-define each other.. > > fourth, perhaps you could show LINE BY LINE how > phi(x) <-> x ~e x > > is barred from inferring an existent set B. > > Herc > -- > EARTH, WIND, FIRE, WATER... is my bet!
its possible at some during the development of alphanumeric symbols 'phi' and 'rho' would have been ceremoniously expunged from certain documents when the ancient Egyptian civilizations began to fall. The very earliest are simple geometries you could calculate multiplications, triganometries, etc. The Etruscians and early Western Euorpeans had their own very early phonemic script, but that didnt develop. Digamma. San, Koppa are all missing from classical Greek.
As a matter of strict importance the solar year is 365 days long, not 360 degrees, and they wernt soft in the ed.