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# Topic: Null set

###### In the News (Thu 23 May 13)

 Null set - Wikipedia, the free encyclopedia In measure theory, a null set is a set that is negligible for the purposes of the measure in question. In particular, the set Q of rational numbers is a null set, despite being dense in R. Null sets play a key role in the definition of the Lebesgue integral: if functions f and g are equal except on a null set, then f is integrable if and only if g is, and their integrals are equal. en.wikipedia.org /wiki/Null_set   (543 words)

 Empty set - Wikipedia, the free encyclopedia In axiomatic set theory it is postulated to exist by the axiom of empty set and all finite sets are constructed from it. All its boundary points (of which there are none) are in the empty set, and the set is therefore closed; while all its interior points (of which there are again none) are in the empty set, and the set is therefore open. In the axiomatization of set theory known as Zermelo-Fraenkel set theory, the existence of the empty set is assured by the axiom of empty set. en.wikipedia.org /wiki/Empty_set   (1416 words)

 PlanetMath: empty set   (Site not responding. Last check: 2007-10-07) The Zermelo-Fraenkel Axioms of set theory imply that there exists an empty set. An empty set is a subset of every other set, and any two empty sets are equal. This is version 3 of empty set, born on 2001-10-19, modified 2004-04-05. planetmath.org /encyclopedia/NullSet.html   (90 words)

 null set - a Whatis.com definition - see also: empty set   (Site not responding. Last check: 2007-10-07) In mathematical sets, the null set, also called the empty set, is the set that does not contain anything. The null set makes it possible to explicitly define the results of operations on certain sets that would otherwise not be explicitly definable. In axiomatic mathematics, zero is defined as the cardinality of (that is, the number of elements in) the null set. whatis.techtarget.com /definition/0,,sid9_gci840849,00.html   (213 words)

 Null set   (Site not responding. Last check: 2007-10-07) In measure theory, a null set is a set which is neglible for the purposes of the measure in question. Let X be a measurable space, let m be a measure on X, and let N be a measurable set[?] in X. A nonmeasurable set is considered null if it's a subset of a null measurable set. www.websign.sk /nu/Null_set.html   (376 words)

 filmcritic.com Null Set Productions Home Page   (Site not responding. Last check: 2007-10-07) Null Set Productions was founded in 1996 to develop and produce feature films and short subject works without the hassle, cost, and time delays of the traditional Hollywood scene. The company was formed by Christopher Null (writer, producer, and occassional actor) and his brother Bradley Null (director and editor). Null Set Productions (in association with Akron Productions) is currently in post-production on a 60-second commercial for the Web for icPlanet. www.filmcritic.com /misc/emporium.nsf/WebPages/nullset   (902 words)

 PHP: is_null - Manual I have variables that may be set to empty (\$test = "";) when passed into a fuction and as such may be set, but not null, but still empty. We can conclude that is_null will error on an unset variable, and thus is not the same as isset. Regarding avoidance of NULLs in your MySQL queries, why not use IS NULL and IS NOT NULL in your WHERE clauses. us3.php.net /is_null   (653 words)

 SortedSet (Java 2 Platform SE v1.4.2) A set that further guarantees that its iterator will traverse the set in ascending element order, sorted according to the natural ordering of its elements (see Comparable), or by a Comparator provided at sorted set creation time. All elements inserted into an sorted set must implement the Comparable interface (or be accepted by the specified Comparator). The returned sorted set is backed by this sorted set, so changes in the returned sorted set are reflected in this sorted set, and vice-versa. java.sun.com /j2se/1.4.1/docs/api/java/util/SortedSet.html   (1168 words)

 [No title] PROOF: The set of points of discontinuity of any function forms an F_sigma set (can be written as a countable union of closed sets), and it is easy to see that any F_sigma Lebesgue null set is also first category. Therefore, the collection of sigma-Jordan null sets is a sigma-ideal that is contained in the sigma-ideal of sets simultaneously Lebesgue null and first category. Finally, the construction of such a set is briefly outlined by Lipinski [11] in 1972, the paper Balcerzak, Baumgartner, and Hejduk [2] refer to for such a set. www.math.niu.edu /~rusin/known-math/00_incoming/lebesgue   (2146 words)

 PHP: NULL - Manual Finally, for those who do not know SQL: in SQL the NULL value is evaluated a bit like "I do not know; it could be anything, like 0, 1, a, b, true, false or even nothing at all". Nulls are almost the same as unset variables and it is hard to tell the difference without creating errors from the interpreter: So, in most cases I found that we needed to use !isset(\$var) intead of is_null(\$var) and then set \$var = NULL if the variable needs to be used later to guarantee that \$var is a valid variable with a NULL value instead of being undefined. www.php.net /manual/en/language.types.null.php   (648 words)

 .NET GC Myth #1 -- Set Object to Null   (Site not responding. Last check: 2007-10-07) There is never any reason to setting your objects to null (or nothing in VB) since the GC will do this for you automatically. Just that while you may not “need” to set your objects to null, there are some cases where you can realize significant gains by being preemptive and setting your large objects to null when you know they are no longer needed. Setting Object To Null is usually not necessary, because the JIT compiler tracks the LAST use of a variable within a method. weblogs.asp.net /pwilson/archive/2004/02/20/77422.aspx   (1785 words)

 The Null Set: Puzzles and Games: Mathematical Puzzles   (Site not responding. Last check: 2007-10-07) Show a 3D closed convex object, such that the set of its extremal points is not closed. Show that in any non countable subset of the line, there is at least one point in the set, that is an accumulation point of it. Prove that any closed subset of the real line, is the zero set of an infinitely derivable function (maybe you would like to prove it for a continuous function first). www.princeton.edu /~mathclub/puzzles4.html   (400 words)

 Math Forum - Ask Dr. Math   (Site not responding. Last check: 2007-10-07) We were talking about sets and he told us that the null set is a subset of every set, but he couldn't remember if it was a * proper* subset of every set. every set is a subset of itself), the null set is a subset of the null set. But this containment is not proper; thus the null set is not a proper subset of every set. mathforum.org /library/drmath/view/52402.html   (170 words)

 Untitled The null set is always a member of every set. The power set of a set S, is a set of all the subsets of S. This is written as P(S). A power set is basically every combination of the elements within a given set, each on their own set, including the null set. cse.unl.edu /~aebbeka/sets/p4.html   (324 words)

 PHPBuilder.com - Differentiate between not set and NULL As far as I can tell NULL and not set are just about the same. So if you rely on a script that may or may not set a variable or array index (which would indicate whether or not that variable or index was in fact processed by that script), then testing for the difference between never set and set but NULL could be valuable. NULL can't mean "never been set" if you can set it to NULL in the first place. www.phpbuilder.com /board/showthread.php?p=10648203   (1216 words)

 Brad Abrams : To set to Nothing (null) or not... Admittly this will only happen when the GC happens to kick off while the method is runnning but before the statements that null the variable are reached, so the effect would be minimal to say the least for almost all cases. I'm in agreement that setting to null should be the exception, but I've also posted sample code that proved it can make a big difference at times and its been frustrating to see some people not want to acknowledge that -- so great post -- very well balanced. Basically setting to Nothing in the right order fixed some refcounting issues with the ADO classes in a particular version. blogs.msdn.com /brada/archive/2004/05/24/140645.aspx   (827 words)

 Exploring 'ON DELETE SET NULL' in SQL Server 2005 At first glance, the 'ON DELETE SET NULL' option in SQL Server 2005 may not seem like a big deal, but once you've seen how it can be used, I think you will be impressed. It allows the "parent" record to be deleted and sets the "child" record's column to NULL. This meant that a sign-on ID that had been deleted could not be used again as long as the "soft" deleted record remained in the table (due to a unique constraint on the SignonID column). www.sqljunkies.com /Tutorial/D839595A-0BC3-4F7E-97EA-DE4911EE2217.scuk   (670 words)

 Splendid E-zine reviews: The Null Set With an ear for Louisville-based math rock, this Irish trio delve into such delicacies as Rodan's stop-start riffing, brooding and dreamy Wire-inspired dirges and roaring, noise-fests a la Jackonuts. As the record needle parses from track to track, the Null Set offers a bit of everything for everyone. Teeming with creativity, The Null Set satiates cravings for fresh, unknown talent, European exoticism and intelligently versed indie rock -- all within the confines of a humbly released 10". www.splendidezine.com /reviews/aug-2-99/null.html   (168 words)

 Lipschitz Image of a Measure--null Set Can Have a Null Complement (ResearchIndex)   (Site not responding. Last check: 2007-10-07) We give two examples that in infinite dimensional Banach spaces the measure-null sets are not preserved by Lipschitz homeomorphisms. There exists a closed set D ae ` 2 which contains a translate of any compact set in the unit ball of ` 2 and a Lipschitz isomorphism F of ` 2 onto ` 2 so that F (D) is contained in a hyperplane. There exists a Borel set A ae X and a Lipschitz isomorphism F of X onto itself so that the sets X n A and F (A) are... citeseer.ist.psu.edu /288500.html   (249 words)

 Son of Devil's Advocate Some care is needed in defining a set that can't possibly have a member. No way -- the NULL set, be told, is a valid member of other non-empty sets, but NULL itself is empty. I've set the yellow one at page 88, which urges the use of a literal 0 rather than the deprecated C-tainted macro NULL. www.sarcheck.com /skb/soda0006.htm   (2394 words)

 Set Field to Null in Sql Server Enterprise Manager Result Set   (Site not responding. Last check: 2007-10-07) Have you ever edited a result set in Enterprise Manager and wished that there was a way to set a field to null? If you are in the field you want to set null you just hit CTRL-0 and leave the field and magically the field has a null value, of course you can only do this on fields that are actually nullable. What I have done before is enter some text then leave the row, then go back and delete the text. weblogs.asp.net /whaggard/archive/2003/10/19/32495.aspx   (390 words)

 null set - OneLook Dictionary Search Tip: Click on the first link on a line below to go directly to a page where "null set" is defined. Null Set : Eric Weisstein's World of Mathematics [home, info] noun: a set that is empty; a set with no members www.onelook.com /cgi-bin/cgiwrap/bware/dofind.cgi?word=null+set   (130 words)

 [No title] return } set %moo Hunt \$+ \$1 if (\$isalias(%moo)) { a e Sorry, that name (\$+ \$1 \$+) is reserved for the script. return } if (\$2 == \$null) { huntdel \$1 return } set %L \$len(\$2-) if (%L > 470) { a e Max safe size is 470 characters, you have %L \$+. huntdone } set %ht.CN \$gettok(%ht.C,0,32) a 5,99 \$+ %ht.CN of %ht.BN passed /userhost (not set away, not nickserv enforcers). www.palosverdes.com /jesse/irc/hunt.txt   (682 words)

 Mozilla LDAP C SDK: Chapter 16 - Writing Multithreaded Clients If you are writing a multi-threaded client where different threads access the same LDAP structure, you need to set up the session so that the threads do not interfere with each other. In a multi-threaded client, you need to set up the session so that each thread can have its own error code. structure identifying the functions that are called in multi-threaded environments (for example, functions to lock and unlock critical sections of code and to get and set errors). www.mozilla.org /directory/csdk-docs/threaded.htm   (1276 words)

 [No title]   (Site not responding. Last check: 2007-10-07) */ if (argv[0] == NULL) { sqlite_set_result_string(pfn, NULL, 0); } else { char hexstr[32]; char sign = +1; const char *h = argv[0]; int hexval; /* Skip over a leading sign character. ** strtol() requires format [(+-)]0x[0-9a-fA-F]+ */ sprintf(hexstr, "0x%s", h); hexval = (int)strtol(hexstr, NULL, 16); sqlite_set_result_int(pfn, hexval); } } /* ** Convert a decimal integer to a hexadecimal string. */ if (argv[0] == NULL) { sqlite_set_result_string(pfn, NULL, 0); } else { char hexstr[32]; int val = atoi(argv[0]); sprintf(hexstr, "%x", val); sqlite_set_result_string(pfn, hexstr, -1); } } /* ** Reverse the contents of a string. web.utk.edu /~jplyon/sqlite/code/sqaux-userfns.c   (1037 words)

 How to set a NULL value through the VCL How to set a NULL value through the VCL I need to set a field in a record back to NULL (not an empty string or 0 for a numeric field). To set a field to NULL, you need to use the www.delphifaq.com /faq/delphi/database/f56.shtml   (107 words)

 4.7 Implementation with a search tree right if (sub[1] == null) return sub[0]; // nothing at right... while (e.sub[1] != null) e = e.sub[1]; //...move to it's bottom right e.sub[1] = sub[1]; //...and attach my right there return sub[0]; //...all is below left } /** adjust count by current element. /** this.sub[at] is null and should be Element(x). www.cs.rit.edu /~ats/java-2001-1/html/skript-27.html   (888 words)

 Aleph Naught and the Null Set One example of these would be the integer set. The empty set; the null set is a set with no contents. If you create your own music, I'd love to hear it - either email me with a web link or send me a cassette or CD please. www.alephnaught.com /AlephNaught.html   (275 words)

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