[QUOTE=davar55;248345]The wording is poor but comprehensible.

You're definitely on the right track.

I don't yet know what to suggest except try re-wording.[/QUOTE]

basically each square can either be black or white if we follow from a supposedly black square we can go to either a square saying it's white or black this creates 2^25 paths of choosing black or white for each square not all are correct. the formula in number freak refers to a pattern described under # 70 in which a square is divided into 8 isosceles right triangles. binary logic then suggest the answer to the question how many designs are there? should be 2^8 but that's not accurate, it doesn't allow for rotations and reflections , it then explains that by that reckoning 256/4 = 64 sounds tempting but symmetries destroy that possibility, because an all white or all black design when rotated never changes. it then introduces a rewording of what they call "Burnsides lemma" ( though they admit he supposedly had nothing to do with it, as it was developed before his time) the rephrasing is as such, [QUOTE]the idea is that you start with the total number of designs (256), add the number of designs that are symmetric with respect to 180-degree rotations (16), and then add the number that are with respect to 90-degree rotations in either direction (4+4) for a total of 280. Now you can divide by 4 (again the number of possible rotations) to get a grand total of 70 distinct designs[/QUOTE] so I have a formula but I don't know how to find the (16) and (4+4). if I knew that I could likely figure a better estimate with rotations involved.

[QUOTE=davar55;248345]You're definitely on the right track.[/QUOTE]

He's completely on the wrong track.

Edit: His latest post confirms. Completely on the wrong track.

[QUOTE=Mr. P-1;248351]I actually meant De Morgan's laws as they apply to sets.[/QUOTE]

Yes I know.

This law is more fundamental.

[QUOTE=science_man_88;248354]basically each square can either be black or white if we follow from a supposedly black square we can go to either a square saying it's white or black this creates 2^25 paths of choosing black or white for each square not all are correct. the formula in number freak refers to a pattern described under # 70 in which a square is divided into 8 isosceles right triangles. binary logic then suggest the answer to the question how many designs are there? should be 2^8 but that's not accurate, it doesn't allow for rotations and reflections , it then explains that by that reckoning 256/4 = 64 sounds tempting but symmetries destroy that possibility, because an all white or all black design when rotated never changes. it then introduces a rewording of what they call "Burnsides lemma" ( though they admit he supposedly had nothing to do with it, as it was developed before his time) the rephrasing is as such, so I have a formula but I don't know how to find the (16) and (4+4). if I knew that I could likely figure a better estimate with rotations involved.[/QUOTE]

OK for everyone else there are three things going on -

the Law of Excluded Middle
fundaments of set theory
fundaments of combinatorics

Try to keep them straight.

[QUOTE=science_man_88;248284]union: the collection of sets into a bigger set such that all subsets are represented.

intersection: having a element in common between sets.[/QUOTE]

Either you don't understand, what these things are, or you're hopelessly inprecise in explaining your understanding.

Excercise. Complete the following two sentences using one word only:

1. An intersection of sets is a _____.
2. A union of sets is a _____.

Hint: It's the same word in each case.

[QUOTE=Mr. P-1;248362]Either you don't understand, what these things are, or you're hopelessly inprecise in explaining your understanding.

Excercise. Complete the following two sentences using one word only:

1. An intersection of sets is a _____.
2. A union of sets is a _____.

Hint: It's the same word in each case.[/QUOTE]

My quick response is set.

[QUOTE=davar55;248367]My quick response is set.[/QUOTE]

that was my second thought for both. because the intersection of sets is the subset they have in common, a union of sets forms a bigger set.

[QUOTE=science_man_88;248368]that was my second thought for both. because the intersection of sets is the subset they have in common, a union of sets forms a bigger set.[/QUOTE]

Cleverly not mentioning yiour first thought.

[QUOTE=davar55;248367]My quick response is set.[/QUOTE]

Correct.

[QUOTE=science_man_88;248368]that was my second thought for both.[/QUOTE]

What was your first thought?

[QUOTE]because the intersection of sets is the subset they have in common[/QUOTE]

Getting there.

Let A = {1, 2, 3, 4}. Let B = {2, 3, 4, 5}

List all the subsets these two sets have in common. How many are there? Which one is the intersection?

[QUOTE]a union of 2 sets forms a bigger set.[/QUOTE]

What is A union A? Is it bigger than A?

[QUOTE=Mr. P-1;248376]Correct.



What was your first thought?

[COLOR="Red"] my descriptions not including the word set[/COLOR]




Getting there.

Let A = {1, 2, 3, 4}. Let B = {2, 3, 4, 5}

List all the subsets these two sets have in common. How many are there? Which one is the intersection?

[COLOR="Red"]{2},{3},{4},{2,3},{2,4},{3,4},{2,3,4}, and there reversals as well as {3,2,4},{3,4,2},and {4,2,3} ? I'm guessing all of the largest ones could be considered equal and they could [TEX]\therefore[/TEX] all be a version of the intersection [/COLOR]



What is A union A? Is it bigger than A?
[COLOR="Red"]I'm guessing that it's either A+A or the set that captures all [B]distinct[/B] elements in both sets which in this case would be A. [/COLOR]
[/QUOTE]

As you can see I'm not completely sure on them.

[QUOTE=science_man_88;248380]As you can see I'm not completely sure on them.[/QUOTE]

You're definitely getting close.

Sets are unordered, tuples are ordered.