<p>I think this question is more about the semantics of the english language than about cs theory. Unless this has a connection to some problem. I think generally speaking, hierarchy of <em>things</em> just means there is a well ordered relation of these <em>things</em>. And nested just means that the <em>things</em> are nested within each other. The relation is defined based on nesting. So the military ranks are a hierarchy, but not a nested one because the groups aren't nested within each other.</p>

CC BY-SA 4.0
2021-01-06T19:28:44.500Z
Thanks @styopa !  Can I ask a quick follow-up…
A, B, C, and D are sets.  
A includes B.
B includes C and D.
Thus, for nesting-level:
A = 0.
B = 1.
C = 2.
D = 2.
Nesting-level is a total order on A, but it is not a well-order because not every subset of A has a least element.  
A is nested, but can we call it a hierarchy?
Steve_P
CC BY-SA 4.0
2021-01-08T00:08:44.753Z
From the definition of hierarchy I've seen most, I wouldn't call it a hierarchy. However, I don't think this matters for any practical purposes. You could just make a small note before calling it a hierarchy.
styopa
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2021-01-09T06:50:05.097Z
Thank you so much!    @styopa
Steve_P
CC BY-SA 4.0
2021-01-01T19:35:23.863Z
2021-01-01T19:35:23.863Z
styopa
<p>(I didn't see any question like this on the CSTheory exchange -- apologies if it has already been answered.)</p>
<p>In a nested hierarchy, a higher level includes all levels below it.</p>
<p>The classic example of a &quot;non-nested&quot; hierarchy is military rank.  A general is not a lieutenant, so military rank is a non-nested hierarchy.</p>
<p>But here's my objection -- doesn't a general have all the skills a lieutenant has, plus more skills?  So in that sense, isn't every general a lieutenant?  He may not be called &quot;lieutenant&quot;, but in reality he is a lieutenant-plus.</p>
<p>Thus, I am wondering... can we really say that any hierarchy is non-nested?</p>

CC BY-SA 4.0
2020-12-22T18:56:14.203Z
This seems off-topic unless you add a connection to research-level theoretical computer science.
Laakeri
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2020-12-22T21:51:22.273Z
I thought from the title it was going to ask about hierarchies like PH or the W-hierarchy, and whether there are analogous hierarchies that aren't linearly ordered...
Joshua Grochow
CC BY-SA 4.0
2021-01-06T19:27:47.080Z
Sorry guys - I’ll try to move this question to the StackExchange for the English language (or for Math).  I’m a data wrangler rather than a true CS person.
Steve_P
<hierarchy-theorems>
Is there any such thing as a non-nested hierarchy?
Steve_P
# Is there any such thing as a non-nested hierarchy?

(Asked by: username_0 on 2020-12-22)

(I didn't see any question like this on the CSTheory exchange -- apologies if it has already been answered.)

In a nested hierarchy, a higher level includes all levels below it.

The classic example of a "non-nested" hierarchy is military rank. A general is not a lieutenant, so military rank is a non-nested hierarchy.

But here's my objection -- doesn't a general have all the skills a lieutenant has, plus more skills? So in that sense, isn't every general a lieutenant? He may not be called "lieutenant", but in reality he is a lieutenant-plus.

Thus, I am wondering... can we really say that any hierarchy is non-nested?

**Tags:** hierarchy-theorems

> **Comments:**
> **username_1**: This seems off-topic unless you add a connection to research-level theoretical computer science.  
> **username_2**: I thought from the title it was going to ask about hierarchies like PH or the W-hierarchy, and whether there are analogous hierarchies that aren't linearly ordered...  
> **username_0**: Sorry guys - I’ll try to move this question to the StackExchange for the English language (or for Math).  I’m a data wrangler rather than a true CS person.  

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## 1 answers

### Answer by username_3 on 2021-01-01. Score: 0 | Accepted answer

I think this question is more about the semantics of the english language than about cs theory. Unless this has a connection to some problem. I think generally speaking, hierarchy of *things* just means there is a well ordered relation of these *things*. And nested just means that the *things* are nested within each other. The relation is defined based on nesting. So the military ranks are a hierarchy, but not a nested one because the groups aren't nested within each other.

> **Comments:**
> **username_0**: Thanks @username_3 !  Can I ask a quick follow-up… A, B, C, and D are sets.   A includes B. B includes C and D. Thus, for nesting-level: A = 0. B = 1. C = 2. D = 2. Nesting-level is a total order on A, but it is not a well-order because not every subset of A has a least element.   A is nested, but can we call it a hierarchy?  
> **username_3**: From the definition of hierarchy I've seen most, I wouldn't call it a hierarchy. However, I don't think this matters for any practical purposes. You could just make a small note before calling it a hierarchy.  
> **username_0**: Thank you so much!    @username_3  

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