Re: Missing equality operator

William Elliott said:

> How do you express trichotomy?
> Without expressing that axiom, then
> not a < b and not b < a

Maybe you need to state the kinds of things you might expect to start
with as axioms.

Actually there is a potential application for an axiom system without
equality. As a general rule, when writing numerical algorithms it's a
bad idea to compare two floating point numbers for exact equality
because numbers that 'ought' to be equal may fail to be because of
rounding errors, even if computed from exactly the same expressions.
Often a fuzzy approximate equality test works better.

.

Relevant Pages

  • Re: ZFC means?
    ... > There is no axiom of set theory that says that is a set. ... respect to expressing a relation for program synthesis which you ... judge of those who misuse terminology!: "No, ... then you are saying that any subset of any set is a set. ...
    (sci.logic)
  • Re: What is a proof, exactly?
    ... so the first thing one can with the axiom ... and formulas without equality. ... They may have the same members, ... distinguish a set that contains AN empty set from a set that contains ...
    (sci.math)
  • Re: tedious sledding re set existence in FOL
    ... > If you start out with the usual definition of set equality ... > to doing this in FOL withOUT equality, ... photocopied page) describes the situation as "Extensionality assures us ... perhaps this axiom could be dispensed with. ...
    (sci.logic)
  • Re: Are you guys really such a bunch of wimps .....
    ... left of the equality sign is not equal to the ' 1 ' on the right of the ... Maybe what we need here one of the Harris Axioms. ... An Axiom of James Harris ... Existence implies uniqueness. ...
    (sci.math)
  • Re: The versatility of A = A
    ... place, equal, and not because of the axiom of equality. ... I can encode the yellow of a ... derived theorem because it is so simple (and difficult to split up ...
    (sci.logic)