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2011-01-25, 17:33   #298
Mr. P-1

Jun 2003

7·167 Posts

Quote:
 Originally Posted by davar55 Infinity ... is not a "Real Number" as in the closure of the rational numbers.
The real numbers are the completion of the rational numbers. Closure is a different concept.

2011-01-25, 17:53   #299
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

26×131 Posts

Quote:
 Originally Posted by Mr. P-1 1)Try to complete this sentence: A partition on S is a collection of ______ of S, such that ... OK for now. Perfect. A collection is a set of sets. That means that everything you know about sets applies to collections too. The word "group" has a technical meaning in mathematics and really shouldn't be used, even informally, to mean anything else.
1) Pairwise disjoint subsets of S, would be my best guess.

dearly noted on the word group I just didn't see set as a possibility but I should have though of the fact that the sets are subsets of the collection.

2011-01-25, 18:03   #300
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

26·131 Posts

Quote:
 Originally Posted by Mr. P-1 An intersection between two sets is the set whose elements are just the elements that the two sets have in common. We haven't talked about it yet, but how do you think you could define the intersection of a collection of sets? Complete the following sentence: The union of two sets is the set whose elements are...the distinct elements of A and B such that no overlap occurs. Try to define the union of a collection of sets. the collection itself with all duplicates thrown away ? Formally defining an n-tuple require concepts more advanced than we've discussed. Informally, an n-tuple is an ordered set of n not necessarily distinct elements. Complete the following sentence: A Cartesian product A x B of two sets is the set of all ordered pairs(a, b) with a$\in$A and b in B (Hard) How would you define a Cartesian product on an n-tuple of sets? What's a relation? What kind of things? good god I'm screwed I can't figure a way to answer either , especially describing a relation without using the word relation. Perfect (assuming you can define reflexive symmetric and transitive). As I said, I think you're making great progress.
here's what you wanted as feedback, assuming feedback isn't negative.

Last fiddled with by science_man_88 on 2011-01-25 at 18:06

2011-01-25, 18:16   #301
Chris Card

Aug 2004

3×43 Posts

Quote:
 Originally Posted by science_man_88 What's a relation? What kind of things? good god I'm screwed I can't figure a way to answer either , especially describing a relation without using the word relation.
Something like "a relation between two sets A and B is a subset of the Cartesian product A x B"?

Chris

Last fiddled with by Chris Card on 2011-01-25 at 18:16

2011-01-25, 18:51   #302
xilman
Bamboozled!

May 2003
Down not across

2·712 Posts

Quote:
 Originally Posted by Mr. P-1 Not to me. At least, if he has, then I'd be concerned about the quality of the source. Although a considerable improvement upon his previous efforts, his definitions still lack precision, leaving me uncertain whether he doesn't properly understand the concepts, or he does, but just can't explain them precisely. More and more I find myself leaning toward the latter, which is a clear indication of progress.
Ok, I'm quite prepared to admit that I may be wrong in this instance. If so, I apologise to sm88 for my statement.

Paul

2011-01-25, 18:54   #303
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

26·131 Posts

Quote:
 Originally Posted by xilman Ok, I'm quite prepared to admit that I may be wrong in this instance. If so, I apologise to sm88 for my statement. Paul
paul I like memorization so I should be able to memorize book like definitions so I don't blame you.

2011-01-25, 20:38   #304
davar55

May 2004
New York City

10000100000112 Posts

Quote:
 Originally Posted by Mr. P-1 The real numbers are the completion of the rational numbers. Closure is a different concept.
@P-1: For me at least please define both as you see the difference.

2011-01-25, 22:37   #305
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

26·131 Posts

Quote:
 Originally Posted by davar55 @P-1: For me at least please define both as you see the difference.
http://en.wikipedia.org/wiki/Closure_(mathematics)

I can't find one for completion

2011-01-25, 23:02   #306
CRGreathouse

Aug 2006

586210 Posts

Quote:
 Originally Posted by science_man_88 I can't find one for completion
http://en.wikipedia.org/wiki/Completeness_(order_theory)

http://terrytao.wordpress.com/2010/1...dard-analysis/

2011-01-26, 00:08   #307
Mr. P-1

Jun 2003

22218 Posts

Quote:
 Originally Posted by CRGreathouse
And, for the sake of, er, completion, this:

http://en.wikipedia.org/wiki/Complet...ace#Completion

2011-01-26, 00:11   #308
R.D. Silverman

Nov 2003

25·233 Posts

Quote:
 Originally Posted by Mr. P-1 And, for the sake of, er, completion, this: http://en.wikipedia.org/wiki/Complet...ace#Completion

The intermediate value theorem strikes again!

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