Re: Is {{}} a valid construct?

Neo <neo55592_at_hotmail.com> wrote:
> > So the thing is, the one who made up this flawed example is you.
>
> The problem is, it's not just me. Anyone can repeat the above example
> of adding nothing and see the discrepancy between reality and set
> theory.

I can't. What I can reproduce is that sloppy use of English is confusing. What do you mean by "add nothing to the box"? If you mean that the SET of things you add is {}, then the resulting set is { apple, orange }. If you mean that you add the empty set, then the result is { apple, orange, {} }. These are two different things. As you noted, the first contains two things but the second contains three things.

Perhaps it would be clearer to you if we remove the empty set from the discussion. Lets say you "add a pear and a grape to the box". Does this mean that { pear, grape } is the SET of things that you add? If so, then the result is { apple, orange, pear, grape }. But if you meant that you add { pear, grape } *as a set*, then the result is instead { apple, orange, { pear, grape } }. The first set contains four things, but the second set contains only three things.

Set theory does not incorporate any interpretation of English sentences. Therefore, no one's sloppy use of language is in any way a discrepancy with set theory.

-- 
Chris Smith