# Troubled with Definition

1. May 17, 2010

### annoymage

1. The problem statement, all variables and given/known data

extension theorem

"A "subsentence" of a given sentence is a sentence that‘s a part of the given sentence, where we count a sentence as a part of itself. A "proper subsentence" of a given sentence is a subsentence of the given sentence other than itself."

i don't understand "subsentence of the given sentence other than itself"

could anyone give me some example to make me understand?

i'm studying mathematical logic, but i think this question is more to language than math.
I don't know if it is legal to post question like this, since i don't know any active linguistic forum,and lazy to find one, ;P, i hope someone help me with this. and if it is illegal, tell me.

Last edited: May 17, 2010
2. May 17, 2010

### D H

Staff Emeritus
Two sentences, A and B
• A does not contain a proper subsentence.
• B is a bit more verbose; it contains two proper subsentences.

The whole is a part (a trivial part) of the whole. Thus sentence A contains a subsentence (sentence A itself), but it does not contain a proper subsentence. Snip any part off of sentence A and you no longer have something that obeys the rules of grammar as to what constitutes a sentence. Now look at the two phrases in Sentence B, "B is a bit more verbose" and "it contains two proper subsentences." Both of these phrases follow the rules of grammar for what constitutes a sentence. They are sentences in and of themselves. They are proper subsentences.

3. May 17, 2010

### annoymage

yes, yes i get it now, thank you :D

4. May 18, 2010

### annoymage

sorry, but this bugging me

"The only subsentence of (φ ∨ ψ) other than (φ ∨ ψ) itself are the subsentences of φ and the subsentences of ψ." (i pick this from lecture note)

is that mean φ and ψ is a "proper subsentence"?

if it is, it's clearly said that φ and ψ is a "subsentence"

so, meaning every "proper subsentence" is a subset of "subsentence"???

5. May 18, 2010

### annoymage

hey of course it is, "..is a subsentence of the given sentence other than itself." (clearly said from definiton, sorry)

but still i confused with "given sentence other than itself"

6. May 18, 2010

### hgfalling

A comma would make it more clear.

A proper subsentence is a subsentence of the given sentence, other than itself.

or

A proper subsentence is any subsentence of a given sentence, except that the given sentence is not a proper subsentence of itself.

that clearer?

7. May 18, 2010

### annoymage

Yesss, very clear. thanks :D