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Off Topic: Question about OT | 439 comments | Create New Account
Comments belong to whoever posts them. Please notify us of inappropriate comments.
Off Topic: Question about OT
Authored by: Anonymous on Monday, May 14 2012 @ 04:37 PM EDT
That's an easy one.

When a distinguished scientist observes facts that match his beliefs, that's a
set theory.

When a young whippersnapper comes along with facts that don't match, that an
upset theory.

John Macdonald

[ Reply to This | Parent | # ]

With Apologies to Godel - Explaning Set Theory
Authored by: Anonymous on Monday, May 14 2012 @ 06:34 PM EDT
https://en.wikipedia.org/wiki/Set_theory

Set theory starts with the set. A set is a collection of things. What sort of
things? Whatever you want, pretty much (numbers, other sets, edges, vertices,
etc.). We make up more rules later. Imagine a set as a bag that we cram full
of other things (numbers, other bags, etc.). Then we define operations upon
that set. That is, stuff you can do to the bag. First up is the "element
of" operator which tells us if a set contains some object. Take your bag
and look inside. Is the object in there? If so, it's an element of that bag,
err, set.

Then there's a very unique thing called the empty set. For any object you give
me, it's not an element of the empty set. No matter what you're looking for in
this bag, it's not in there. But remember, sets can contain other sets... even
empty sets. So a set containing the empty set is not the empty set, just as a
bag containing another empty bag isn't empty. Confused yet?

Now we can have the union of two sets. Imagine dumping the contents of two bags
into a third and removing duplicates. If our object x is an element of S1 or
S2, then it's in S1 union S2. Intersection is similar, but we're making a third
bag that contains only objects that S1 and S2 already contained, so we only put
it in the union if it's an element of S1 and it's an element of S2. It's like
we took the dupes from that union and put them in their own bag. With me so
far?

Basically, after that, you start defining a lot more rules and operations about
what you stuff into bags, err, sets. At no time do you discuss
"dynamic" or "static" optimizations to programs, though.
You probably could use set theory to model a program's execution, but even if we
did, we'd use the normal definitions of symbolic reference and static/dynamic
optimization, not the weird Oracle definitions.

[ Reply to This | Parent | # ]

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