Re: Galileo's Paradox and the Project of the Reals


Tony Orlow wrote:
David Marcus wrote:
Tony Orlow wrote:
No, there are DIFFERENT uses of the word 'successor', as I took
ELABORATE pains to explain to you, and you now are just ignoring.
There is one general definition of successor(x): the element after x.

What does "general definition" mean?


One that is correct regardless of context.

What does it mean for a definition to be "correct"?

(3) A 2-place predicate symbol: x is an R-immediate successor of y (the
variables are 'x' and 'y' while here 'R' is not a variable but rather a
defined constant). Again, no mention of '<', and again, the orginal
formulation does not depend on any SUBSEQUENT informal abbreviations.

Get it through your MASSIVELY thick skull already: All formulas of set
theory revert to the pure language with just the one non-logical
predicate symbol 'e'.
And S().

So, when you say "ZF" or "Z", you mean something different than
mathematicians mean. Are there any words that you use the standard
definitions for? Please state your version of "set theory".


When have I ever said "Z" or "ZF" or "ZFC"? Only on rare occasions when
clarifying what's "true" in that/those theorie(s).

We are discussing Z set theories when we claim "all formulas of set
theory revert to just logic and 'e'". And presumably you are discussing
Z set theories when you dispute that claim. No?

--
mike.

.