Re: Missing equality operator

David R Tribble originally asked, in an earlier usenet post, now lost
to all but the most persistent of clerical backtrackers, the following
question:

> Are there any interesting number theories derived from the basic
> arithmetic axioms while omitting the equality (reflexive) operator?
> I.e., can we create an arithmetic system with the usual '+', 'x',
> an '<' operators and the usual '0' and '1' identities but omit the
> '=' equality operator?

Define a = b if neither a<b nor a>b. So '=' can be defined in terms of
'<'. Hence '=' is already redundant and it makes no difference if you
drop '='.

.