Re: Cantor's definition of set

On Oct 30, 12:16 pm, MoeBlee <jazzm...@xxxxxxxxxxx> wrote:
On Oct 30, 2:56 am, John Jones <jonescard...@xxxxxxx> wrote:

Most definitions seem to rely on being
able to tell left from right.

Not the definition of ordered pair, in the sense that

{{x} {x y}} =
{{x} {y x}} =
{{x y} {x}} =
{{y x} {x}}.

Of course, though, we do stipulate that printed formulas are read from
left to right. But we could as well stipulate the opposite.

Apparently what Laughing Boy is trying to do is sow confusion
at the level of distinguishing syntax from semantics. The syntax
of set theory is strings of symbols, and these strings are of
course ordered. The semantics of set theory is unordered.
Maybe he hopes he can confuse some people on this point.

In addition to writing our strings right to left, we could also
use a representation that is reminiscent of the abstract syntax
tree. We could, for example, use shapes and containment.
So the outermost node in the tree would be the largest shape,
containing all the others. The first child node would be a circle and
subsequent ones would be squares. Child nodes would all be
in a chain, with each node having at least one point in common
with its neighbor(s). Nodes could have any size, position, or
orientation as long as they respected the above, making it
clear that left/right or related concepts are irrelevant.
Of course, Laughing Boy will now just object that telling a
circle and a square apart is hard, or some such lunacy.
Or he'll change the subject again; he does that a lot.


Marshall

.

Relevant Pages

  • Re: Performance of REGEXP_LIKE vs LIKE?
    ... There are certain situations where the syntax of REGEXP_LIKE ... is cleaner and shorter than the comparable LIKE expression. ... search of a 3 million record table, for a series of text strings. ... How about Oracle Text? ...
    (comp.databases.oracle.misc)
  • Re: Proposal for adding symbols within Python
    ... I don't like any syntax I've seen so far, but I can understand the problem. ... (Rather than a string used as a key in that namespace) ... Often you can use strings for that sort of thing, ... The reason I'm more interested in seeing usecases, ...
    (comp.lang.python)
  • Re: Array difference
    ... is there any logical reason why the language doesn't ... but they plan on having a syntax like this. ... use the initialization syntax for the String array. ... Which declares that the method accepts a variable number of strings. ...
    (comp.lang.java.programmer)
  • Re: switch(true) in c#
    ... switch statements evaluate strings, they don't work on boolean variables. ... have a look at the syntax for it in the helpfile and work your code ...
    (microsoft.public.dotnet.framework.aspnet)