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Suppose we define (n) as follows: If n is an integer from 0 to 20, inclusive, then (n) is the number of letters in the English spelling of the number n; otherwise, (n) is undefined. For example, (11)=6 because "eleven" has six letters, but (23) is undefined, because 23 is not an integer from 0 to 20

How many numbers are in the domain of (n) but not in the range of (n)?

 

Suppose we define $\ell(n)$ as follows: If $n$ is an integer from $0$ to $20,$ inclusive, then $\ell(n)$ is the number of letters in the English spelling of the number $n;$ otherwise, $\ell(n)$ is undefined. For example, $\ell(11)=6,$ because "eleven" has six letters, but $\ell(23)$ is undefined, because $23$ is not an integer from $0$ to $20.$

How many numbers are in the domain of $\ell(n)$ but not the range of $\ell(n)?$

 Mar 18, 2019
 #1
avatar+6252 
+3

There's no comprehensive formula for the number of letters in the English spelling of a given number.

So you've got to just list them all out and check.

 

The range of (n) is (3,4,,8)Thus |(1,2)(9,10,,20)|=14is the number you are after

 Mar 18, 2019
edited by Rom  Mar 18, 2019
 #2
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Hmmm...That was incorrect...

Guest Mar 18, 2019
 #3
avatar+6252 
+2

Ok, I spelled eighteen wrong.

 

9 isn't in the range either.  So 14 are in the domain and not in the range.

 

Sorry for the confusion.

Rom  Mar 18, 2019
 #4
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Okay thanks.  That was right!

Guest Mar 19, 2019

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