Talk:Discrete Mathematics/Set theory

elements and members
Should the discussion under notation refer to the example number as an element of the set of a member of the set? ... LouI


 * I assume you mean to say that 3 is an element of the set or a member of the set? Yes, either terminology is acceptable...thank you for jogging my memory :)
 * If that's not what you meant, please clarify, as I don't think I understand you correctly. Dysprosia 22:46, 13 Aug 2003 (UTC)

page moved
I have moved Set theory back to where it was before. Set theory is intended as a purely introductory text, and putting further higher level article links with Set theory disturbs the gradual nature of increase of difficulty as the articles will follow... I hope this is okay with everyone :) Dysprosia 10:27, 14 Aug 2003 (UTC)

questions / answers numbering
The numbering of the questions (section 2.6) doesn't make sense, and some of the answers don't seem to match the questions.

There was a stupid error (probably of mine :) that inserted a carriage return which mucked up the ordering of the numbers. It should be better now. Dysprosia 09:30, 8 Nov 2003 (UTC)

Venn diagrams
Shall I draw some ? If yes what would you like ? Theresa knott 14:42, 2 Feb 2004 (UTC)

Don't ask it, do it. And put them here, too. The one you are asking if she/he would like you drawing pictures to may not look at this section never again. You cannot know. So go and do it (supposing that you know about what you are doing).

--80.220.156.128 21:20, 9 September 2005 (UTC)

ambiguity in section 2.4
I think that section 2.4 is a little unclear

the line reading

Now, B contains some elements of A, but not necessarily all.

could be interpreted to mean that B contains some elements of A in addition to some other elements (not belonging to A)

I suggest

Now, B is made up of elements of A, but not necessarily all


 * I've reworded it in a different way, so it's a bit more clear. Dysprosia 09:02, 19 Oct 2004 (UTC)

How about we say that B is a subset of A if every element of B is also an element of A? Or, equivalently, B doesn't have any elements that aren't also elements of A? (The formation with the double negative makes it clearer that the empty set is a subset of all sets.)

overstatement
"Note that :
 * $$\{x \in \mathbb{N}|\, ax^2+bx+c = 0\}$$

is a completely different set!"

Is a bit of an overstatement...it's actually a subset, not a completeley different set.


 * That is nitpicking a bit. The idea is still there. Though a different example might be called for. Dysprosia 09:15, 29 Jan 2005 (UTC)

problem set: proper subset
I changed the $$\subset$$ signs in problems 3 and 4 to $$\subseteq$$ signs. You can show that A $$\subset$$ B is false by showing that A = B in addition to showing that there is an element of A that is not in B.

problem set: no pun intended?

pointing
In the first paragraph, I changed "your pointing is called a set" to "what you are pointing to is called a set". A set consists of its members. A pointing consists of a (possibly metaphorical) extension of the index finger. Actually, there is a lot of pointing talk in this module that strikes me as a little troubling. Perhaps this should be changed.

(I also added titles to the first two comments of this talk page so the contents box would appear in the right place.)

set comprehension, problem 3
I'm kind of a newbie, so maybe I'm missing something obvious, but in number 3 the first set would start with 2, whereas the second set would start with 1 as the minimum value. Why are they equal?

Never mind, I got it. Duh.

Definitions of Union, Intersection and Difference
I have simplified the definitions of union and intersection, making them more consistent with the notation used in logic, and clarified the example of difference, where the definition referred to B - A, but the example showed A - B. Nigeltn35 (talk) 20:56, 8 November 2008 (UTC)

PS I'm new to using LaTeX. There must be an easier way of writing A - B to get the font and size right!Nigeltn35 (talk) 07:28, 9 November 2008 (UTC)

Introductory Section and Notation
I've attempted a simple introduction, defining a set in terms of 'things' and 'rules'. Have included in the Notations section &isin; and &notin;, and used simple text rather than LaTeX where possible. (IMHO LaTeX looks a bit naff in the default font size!) --Nigeltn35 (talk) 17:28, 9 November 2008 (UTC)

Special Sets
Introduce these special sets before introducing relations between sets and operations on sets, so that an exercise can follow to allow consolidation of basic ideas. Nigeltn35 (talk) 20:17, 9 November 2008 (UTC)

Russell's Paradox
As I understand it, this page is intended as introductory teaching material on Set Theory as part of a Discrete Maths book. Introducing Russell's paradox may be interesting as a bit of background material for Set Theory in general, but I don't really think that it belongs in this text at all. Is there anyone who would vote to keep it in? If not, I propose to remove it. (If anyone wants to keep it, I think it needs re-writing...) Nigeltn35 (talk) 12:01, 21 November 2008 (UTC)

I've finished editing for the time being
I seem to have pretty well completely re-written this stuff on Set Theory. No-one seems to have objected so far. As far as I'm concerned, it's fairly complete. At any rate it will provide a way in to Relations and Functions, Logic, etc. Does anyone else think there's more to do at this stage? If not, what happens to it now? Nigeltn35 (talk) 12:34, 21 November 2008 (UTC)

Page now split into Four Sections
Following a warning message about the size of the file exceeding 32KB, I have split the text up into four sections: the original Set Theory page containing the first half of the teaching material, Page 2 (the remaining teaching material), Exercises and Answers. Nigeltn35 (talk) 12:06, 25 November 2008 (UTC)

Euler diagrams
Venn diagrams are a special case of Euler diagrams, and half of the diagrams in the Venn diagrams section are not Venn diagrams. Some of the instruction also shows how to convert a Venn diagram to a simpler Euler diagram, though it does not use this terminology.

For those who don't know the difference, an Euler diagram may or may not show intersections between sets which are empty, and if an region of exclusivity or intersection between sets is not shown then this is an assertion that the region is empty. For example, if set A is circumscribed by set B, this indicates that all members of A are also members of B. In some cases, Euler diagrams assert that regions which are shown must be non-empty, or at least it is not yet known whether the region is empty.

A Venn diagram is a special case of an Euler diagram that must show all possible intersections and exclusions. So there is only one Venn diagram for three sets (a token of this diagram is shown in Figure 4), but there are many possible Euler diagrams for three sets (in general, 2^2^(n-1) for n sets). TricksterWolf (discuss • contribs) 19:55, 19 November 2011 (UTC)