sm: What axn means is that, using the definition you gave (two people are siblings if they have at least one parent in common), it is possible that A and B are siblings and B and C are siblings but A and C are not siblings. Can you see why? Can you give an example?

[QUOTE=CRGreathouse;249080]sm: What axn means is that, using the definition you gave (two people are siblings if they have at least one parent in common), it is possible that A and B are siblings and B and C are siblings but A and C are not siblings. Can you see why? Can you give an example?[/QUOTE]

yes I see his point, if they aren't on the same side or if the half sibling and the step sibling aren't in the same house they don't fit biological or home.

[QUOTE=science_man_88;249082]yes I see his point, if they aren't on the same side or if the half sibling and the step sibling aren't in the same house they don't fit biological or home.[/QUOTE]

Being in the same house has nothing to do with your definition that I quoted above. Would you give an example that shows the intransitivity of the "sibling" as you defined it in post #133?

[QUOTE=CRGreathouse;249085]Being in the same house has nothing to do with your definition that I quoted above. Would you give an example that shows the intransitivity of the "sibling" as you defined it in post #133?[/QUOTE]

it's intransitive because if you say a sibling must share a parent in there home or biologically either having step or half siblings on both sides or having them on the same side but not in the same house may imply they have no relation as siblings.So case in point there are exceptions to this rule that don't imply the last part hence it's not transitive in these cases, or overall. even without using at home to extend it, it fails.

[QUOTE=science_man_88;249086]it's intransitive because if you say a sibling must share a parent in there home or biologically either having step or half siblings on both sides or having them on the same side but not in the same house may imply they have no relation as siblings.So case in point there are exceptions to this rule that don't imply the last part hence it's not transitive in these cases, or overall. even without using at home to extend it, it fails.[/QUOTE]

A counterexample requires you to give three people such that the first two and the last two are siblings, but the first and last are not siblings.

[QUOTE=CRGreathouse;249095]A counterexample requires you to give three people such that the first two and the last two are siblings, but the first and last are not siblings.[/QUOTE]

I gave 3 non mathematical examples of such a counterexample.

[QUOTE=science_man_88;249132]I gave 3 non mathematical examples of such a counterexample.[/QUOTE]

I think that you may understand the concept, but not how to properly express the counter example.

Try it like this:

Assume that A and B are male parents and that E and F are a female parents.

Further, let X be a child of A x E,
Y be a child of B x E,
Z be a child of B x F.

Now X and Y are siblings because they have a common mother, E.
Further, Y and Z …

Can you finish it?

[QUOTE=Wacky;249134]I think that you may understand the concept, but not how to properly express the counter example.

Try it like this:

Assume that A and B are male parents and that E and F are a female parents.

Further, let X be a child of A x E,
Y be a child of B x E,
Z be a child of B x F.

Now X and Y are siblings because they have a common mother, E.
Further, Y and Z …

Can you finish it?[/QUOTE]

are siblings because they share a parent B , but X and Z aren't considered siblings because they have no at home or biological parents in common.

[QUOTE=xilman;248998]However, the list looks to me as if you have copied and pasted the words from some other source.[/QUOTE]

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.

Take his definition of disjoint for example: "of or pertaining to sets having only [TEX]\empty[/TEX] in common." does he mean that they have [TEX]\empty[/TEX] as a common element? Or a common subset? One of these is correct while the other isn't.

Similarly, his definition of intersection: "the elements that 2 sets have in common.". Actually the intersection is [i]the set[/i] containing just those elements. It's important to understand that an intersection of sets is [i]a set[/i].

[QUOTE=science_man_88;249009]well these are my own attempt but I can still reword them lol. I can't help it if you are good teachers, along with repeated reviewing of the examples in the text Preliminaries.

[B][U]Partition[/U][/B]: making a larger set into smaller subsets such that no 2 subsets intersect.[/QUOTE]

Try to complete this sentence:

A partition on S is a collection of ______ of S, such that ...

[QUOTE][B][U]disjoint[/U][/B]: in such a state that for the sets involved [TEX]\empty = A\cap B[/TEX][/QUOTE]

OK for now.

[QUOTE][B][U]pairwise disjoint[/U][/B]: of all the sets in a collection C such that for all sets [TEX]A,B\in C A\cap B = \empty[/TEX][/QUOTE]

Perfect.

[QUOTE][B][U]Collection[/U][/B] : a group of sets.[/QUOTE]

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.

[QUOTE=science_man_88;248993][B][U]intersection[/U][/B]: the elements that 2 sets have in common.[/QUOTE]

An intersection between two sets is [i]the set[/i] 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?

[QUOTE][B][U]union[/U][/B]: a combining of 2 sets into a larger set containing no duplicates.[/QUOTE]

Complete the following sentence:

The union of two sets is [i]the set[/i] whose elements are...

Try to define the union of a collection of sets.

[QUOTE][B][U]n-tuple[/U][/B]: a ordered group containing a element from n not necessarily disjoint sets.[/QUOTE]

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.

[QUOTE][B][U]Cartesian Product[/U][/B]: the set containing n-tuples to show all combinations withing the elements of n, not necessarily disjoint sets.[/QUOTE]

Complete the following sentence:

A Cartesian product A x B of two sets is the set of all _______ _____ (a, b) with a[TEX]\in[/TEX]A and ___

(Hard) How would you define a Cartesian product on an n-tuple of sets?

[QUOTE][B][U]Binary relation[/U][/B]: a relation connecting 2 things.[/QUOTE]

What's a relation? What kind of things?

[QUOTE][B][U]equivalence relation[/U][/B]: a binary relation that is reflexive, symmetric, and transitive.[/QUOTE]

Perfect (assuming you can define reflexive symmetric and transitive).

[QUOTE]Am I close to correct? found an error I made in these defintions looking back on the thread I think.[/QUOTE]

As I said, I think you're making great progress.