# B Help with determining the order

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1. Feb 13, 2019 at 2:39 PM

### Boltzman Oscillation

Hello guys,

Ive been struggling on determining whether something is ordered or unordered. The example i get is something like, "a burger with pickles, tomato, beef will be the same regardless of the way you make the order." Then in this case it would be ordered right? So when something is ordered then the order doesnt matter? Any help would be appreciated thanks.

2. Feb 13, 2019 at 3:00 PM

### phinds

No, you have it backwards. If it order doesn't matter then it's unordered. If order matters, then it ordered.

The hamburger is a bad example because in reality it's neither. It's true that it doesn't matter the order of the insides (unordered) but it would be quite a mess if you put the tomato and pickles outside the bun.

3. Feb 13, 2019 at 3:01 PM

### Staff: Mentor

While you can buy a burger and the order you specify the ingredients doesnt matter, you do expect them to place the ingredients on the burger in a certain order like:

Bottom bun
Burger
Cheese
Lettuce
Tomota slices
Top bun

Where the bottom bun absorbs the beef juices and the cheese melts over the burger and then the lettuce. ...

4. Feb 13, 2019 at 3:02 PM

### Boltzman Oscillation

So a password would be ordered because the order of each digit matters right?

5. Feb 13, 2019 at 3:02 PM

### phinds

Yes

6. Feb 13, 2019 at 3:03 PM

### Boltzman Oscillation

Bottom bun should be on top of the beef.

7. Feb 13, 2019 at 3:22 PM

### kuruman

That's right. If you order a burger with pickles, tomato and beef, you will get the same thing seved on your plate as if you ordered a burger with beef, tomato and pickles. All jesting aside, before you consider whether something is ordered or not, you have to specify the criteria that you use for what matters. For example, you will agree that the letters in this message are ordered. What if I reordered them putting all like letters together with the punctuation marks and blank spaces in the end. Would that also be ordered or not?

(Here is the reordered message, or is it not ordered?)

8. Feb 13, 2019 at 4:11 PM

### Staff: Mentor

My post is ordered by the steps needed to put the burger together whereas your steps may vary.

9. Feb 13, 2019 at 5:27 PM

### Klystron

Studying combinatorics largely resolved my similar struggles with this question.

A combination is set of objects where member order is not important. In your original example the list of ingredients to prepare a burger plate could be any combination of items in correct proportions, such as buns, patties, cheese slices, etc. Order of the grocery list is not important. (The proportions of each item are important, say 8 buns and 8 patties, but that is a different problem.)

A permutation is set of objects where member order is important. The burger recipe in post 3 permutes the ingredients in a precise order to produce a, no doubt tasty but also consistent, burger order*. If these definitions appear at all self-referential or even recursive, that is not a problem in application such as in probability theory and computer science.

*A burger plate with burger, fried potatoes, and small salad is called a combination plate. Note that the order of the three items on the "combo" is not important.

10. Feb 14, 2019 at 2:24 AM

### Boltzman Oscillation

Hmm well you said that you were putting all the letters first then the punctuation and then the blanks. In that case then I would split the total criteria into three parts, letters, punctuation, and blanks. The criterias are ordered since you HAVE to have letters, punctuation and then blanks. I would then split each criteria into smaller criteria, one for each letter or mark. Am i doing this right?

11. Feb 14, 2019 at 9:31 AM

### kuruman

First of all, "criteria" is plural and its singular is "criterion", one criterion many criteria.

Secondly, I do not believe that the criteria themselves can be ordered. Criteria are just rules. There can be a hierarchy of such rules for conditional ordering. For example, a list of people may be ordered alphabetically by last name; if there are many with the same last name, within that sub-list there may be ordering by first name, then if more than one with the same last and first name order by middle initial, then by email address, etc.

Thirdly, yes you have to have letters and the rest of the stuff. Note that there are additional implicit ordering criteria in my text that you did not mention:
1. All like letters belong together.
2. Capitalized letters are treated the same as lower case letters but there must be a criterion deciding where they go within their group1.
3. The succession of groups of like letters follows the succession of the letters in the English alphabet. Note: On the basis of what criteria was the English alphabet "ordered" anyway?

My point in posting all this is that if you wish to address the issue,
you will first have to choose your criteria of ordering and be aware of all of them. Specifying the criteria is equivalent to specifying what matters to you.

--------------------------------------------
1 To order the text, I imported it in an Excel sheet and parsed out the words into individual rows. Then I parsed the ASCII characters in each word into individual columns. The total number of such columns matched the length of the longest word (=11 in "punctuation"). Then, starting with column 1, I copied and pasted the 11 columns into a single column. Then I alphabetized the contents of that single column. Then I cut and pasted the punctuation marks from the top to the bottom because I wanted them to be there. Finally, I copied and pasted the transpose of the single column to a row which I then pasted into the post. I am mentioning all this because the placement of the capital letters within a group of like letters is implicit in the reordering procedure that I used; there was no randomness involved. Therefore, criteria were used in deciding where the capital letters went. Does the fact that I don't know what those criteria are mean that the ordering of the capital letters "does not matter"? Does the fact that the criteria for ordering the capital letters exist and can be deduced from the process I used mean that the ordering of the capital letters "does matter"? I guess what "matters" is what I care to know about.

12. Feb 14, 2019 at 4:42 PM

### Boltzman Oscillation

yes sir! Thank you!

13. Feb 14, 2019 at 9:21 PM

### sysprog

The order in which ordering criteria are implemented matters in some situations, and not in others. If, for example I want to sort a large classroom by age and gender, with the result that there are two lines of students, one containing all males, and the other containing all females, each line ordered from youngest to oldest, it will be much easier if I do the gender sort before the age sort.