Re: Specifying Sets

Chris Menzel wrote:
an empirically verifiable fact
about the usage of the term in mathematical contexts.

So, according to maths naming convention, a 'shopping list' is a set and not a list. BTW, if this convention flies in the face of common usage don't make sour faces by privileging one use over the other.

So, an unordered collection is not called a list but is called a set. An ordered collection is called a list. Why?

Which different words am I using? The set of all x reduces to all x.

So how would you reduce "The set of all solar planets has nine members"
to a statment about "all solar planets"?

There are 9 solar planets. If we insist on employing the term 'members' then "The set of all solar planets has nine members" reduces to 'set of nine objects', which reduces further to '9'.

'all x' is coherent. 'The set of all x' is not.

There is nothing extravagant is saying "the set of all blondes", above
all if you are doing mathematics.
But as you yourself indicate, there's no difference apart from
convention in saying 'the set of all x' and 'all x'. The former, is therefore extravagent.

The point you seem to be missing is that sets are mathematical objects.

A 'mathematical set' is the sign surrounding glyph {}. There's never been anything else presented beyond that, object-wise.

Reference to them therefore requires locutions like the former. "all x"
does not pick out a set, it simply quantifies over the x's and hence
will not do the job.

If 'all' blondes picks out all blondes, what does the 'set' of all blondes pick out? If you can answer that it will be a surprise, for everything I've seen so far indicates that the term set is used indiscriminately.
.

Relevant Pages

  • Re: Specifying Sets
    ... if this convention flies in the face of common usage ... There are 9 solar planets. ... If we insist on employing the term 'members' ...
    (sci.logic)
  • Re: Is using range() in for loops really Pythonic?
    ... for dummy in range: ... I've never heard of this convention. ... usage I can think of does the word "dummy" suggest something isn't used. ... In mathematics, a dummy argument another name for the independent ...
    (comp.lang.python)
  • Re: simulating local lexical variables with symbol macros
    ... In your previous post you cited a certain usage of `pathological' in ... was using it in the sense used in mathematics. ... what my intention and meaning was. ... false claim on false claim, wronga assumption upon wrong assumption with ...
    (comp.lang.lisp)
  • Re: What languages have huge standard libraries?
    ... >>> neither folklore nor mathematics, but current usage in the context in ... >>> programming languages. ... > words and phrases evolves, and is determined by usage, not ... This is a forum focused on technology. ...
    (comp.programming)
  • Re: Wittgenstein and the philosophy of mathematics
    ... apart from most other philosophies of mathematics. ... truth or falsity to axioms, in mathematics, that our agreeing to work ... matter of convention, but rather something determined as a matter of ... played have no meaning outside the context of the game. ...
    (sci.logic)
Quantcast