[QUOTE=Mr. P-1;248910]Is this remark directed at me or at SM88? I'm well aware that infinity isn't a real number. This is irrelevant because the context of my remark (and SM88's nonsensical manipulations) was cardinal arithmetic.[/QUOTE]

It was an add-on to your remarks.

[QUOTE=R.D. Silverman;248918]It was an add-on to your remarks.[/QUOTE]

Infinity is real in mathematics. (As opposed to unreal.)

It is not a "Real Number" as in the closure of the rational numbers.

Whether the universe contains any "actual infinity" is
a question for cosmology - and philosophy.

[B][U]Partition[/U][/B] :a breakdown of a set down into disjoint subsets.
[B][U]disjoint[/U][/B]: of or pertaining to sets having only [TEX]\empty[/TEX] in common.
[B][U]intersection[/U][/B]: the elements that 2 sets have in common.
[B][U]union[/U][/B]: a combining of 2 sets into a larger set containing no duplicates.
[B][U]n-tuple[/U][/B]: a ordered group containing a element from n not necessarily disjoint sets.
[B][U]collection[/U][/B]: a grouping of sets.
[B][U]pairwise disjoint[/U][/B]: pertaining to a collection having no combination of 2 sets such that there intersection contains anything but [TEX]\empty[/TEX]
[B][U]Cartesian Product[/U][/B]: the set containing n-tuples to show all combinations withing the elements of n, not necessarily disjoint sets.
[B][U]Binary relation[/U][/B]: a relation connecting 2 things.
[B][U]equivalence relation[/U][/B]: a binary relation that is reflexive, symmetric, and transitive.

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

[QUOTE=science_man_88;248993][B][U]Partition[/U][/B] :a breakdown of a set down into disjoint subsets.
[B][U]disjoint[/U][/B]: of or pertaining to sets having only [TEX]\empty[/TEX] in common.
[B][U]intersection[/U][/B]: the elements that 2 sets have in common.
[B][U]union[/U][/B]: a combining of 2 sets into a larger set containing no duplicates.
[B][U]n-tuple[/U][/B]: a ordered group containing a element from n not necessarily disjoint sets.
[B][U]collection[/U][/B]: a grouping of sets.
[B][U]pairwise disjoint[/U][/B]: pertaining to a collection having no combination of 2 sets such that there intersection contains anything but [TEX]\empty[/TEX]
[B][U]Cartesian Product[/U][/B]: the set containing n-tuples to show all combinations withing the elements of n, not necessarily disjoint sets.
[B][U]Binary relation[/U][/B]: a relation connecting 2 things.
[B][U]equivalence relation[/U][/B]: a binary relation that is reflexive, symmetric, and transitive.

Am I close to correct? found an error I made looking back on the thread I think.[/QUOTE]The statements you made are all correct, as far as I know, and it is clear that you have sought out the meanings of the term you give in [B]bold[/B], which is good.

However, the list looks to me as if you have copied and pasted the words from some other source. To show that you understand what each definition [B]means[/B], please repeat your list with the definition in your own words. Paraphrase them, in other words.


Paul

[QUOTE=xilman;248998]The statements you made are all correct, as far as I know, and it is clear that you have sought out the meanings of the term you give in [B]bold[/B], which is good.

However, the list looks to me as if you have copied and pasted the words from some other source. To show that you understand what each definition [B]means[/B], please repeat your list with the definition in your own words. Paraphrase them, in other words.


Paul[/QUOTE]

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


god I'm getting bored of rewording I'll try again later to satisfy your rewording demand.

[QUOTE=science_man_88;249009]
[B][U]disjoint[/U][/B]: in such a state that for the sets involved [TEX]\empty = A\cap B[/TEX][/QUOTE]
Take the case of disjoint. An "English" description would be "Two sets are said to be disjoint if they have no elements in common". This definition doesn't introduce anymore terms than is necessary. Your turn.

[QUOTE=axn;249013]Take the case of disjoint. An "English" description would be "Two sets are said to be disjoint if they have no elements in common". This definition doesn't introduce anymore terms than is necessary. Your turn.[/QUOTE]

actually my rewording looks more like what's in the text than my original wording for disjoint.

[QUOTE=science_man_88;248993][B][U]Partition[/U][/B] :a breakdown of a set down into disjoint subsets.
[B][U]disjoint[/U][/B]: of or pertaining to sets having only [TEX]\empty[/TEX] in common.
[B][U]intersection[/U][/B]: the elements that 2 sets have in common.
[B][U]union[/U][/B]: a combining of 2 sets into a larger set containing no duplicates.
[B][U]n-tuple[/U][/B]: a ordered group containing a element from n not necessarily disjoint sets.
[B][U]collection[/U][/B]: a grouping of sets.
[B][U]pairwise disjoint[/U][/B]: pertaining to a collection having no combination of 2 sets such that there intersection contains anything but [TEX]\empty[/TEX]
[B][U]Cartesian Product[/U][/B]: the set containing n-tuples to show all combinations withing the elements of n, not necessarily disjoint sets.
[B][U]Binary relation[/U][/B]: a relation connecting 2 things.
[B][U]equivalence relation[/U][/B]: a binary relation that is reflexive, symmetric, and transitive.

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

I personally think this is an ok working understanding.

If questions come up later, we can resolve any errors or ambiguities.

[QUOTE=davar55;249038]I personally think this is an ok working understanding.

If questions come up later, we can resolve any errors or ambiguities.[/QUOTE]

my problem isn't that i don't want to reword it for them it's that I don't know if I can without sounding like a book, before it was I didn't know any of it now it's the wording I use, I'm guessing the next one comes as "your brain is wired too much like a coat hanger"

The reason I gave definitions as I understand them is because i couldn't see how connect them all to 1 example to show all of them.

[QUOTE=axn;247941]His analysis is correct, insofar as the set is a very small one lacking any counterexamples. However, if we start with a more realistic set, by his definition, the relation is not transitive (think of step siblings sharing a half sibling).[/QUOTE]

the one case I see it failing is that one if and only if they don't share a house hold or full biology the one reason I agree is I can give an example from my family , if you care to hear it. I believe my dad has official remarried by now so her children are my step siblings and his new kid is my half sibling but the only reason this is not a full case as far as I can see is because they all live in the same house.