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## #1 2006-11-09 23:54:31

Rose-Red
Member
Registered: 2006-01-05
Posts: 19

### Discrete maths - characteristic functions

Hi there,

Here is the question."Let A be the set of 26 letter of the alphabet. Desribe the characteristic function of the set of vowels."
Well the definition of characteristic function seems very simple and I tried to apply it to my question but I'm stuck. I guess I don't understand what exactly I need to do.
Could anyone help me out?

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## #2 2006-11-10 13:29:54

Joel
Member
Registered: 2006-11-09
Posts: 5

### Re: Discrete maths - characteristic functions

Let A={ a,b,c,d......x,y,z}
Let B={ a,e,i,o,u}

Characteristic function is defined as

I(x) = { 1, if x belongs to B,
= { 0, if x doesnot belong to B.      where x is a variable, which can take any letter from the alphabets.

For ex:
If the letter is 'a', then the value is  0.
If the letter is 'e', then the value is  1.

I have given what i know. If u find any mistake, pls correct me.

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## #3 2006-11-12 07:11:42

Rose-Red
Member
Registered: 2006-01-05
Posts: 19

### Re: Discrete maths - characteristic functions

I thought there is 1 if the letter belongs to both set, and 0 if it belongs only to the set A. In this case. letters "a" and "e" both belong to sets A and B, so shouldn't there be 1 in: "If the letter is 'a', then the value is  0."?
Anyway, I understand that, but is this the way I have to describe it? Besides, is letter "y" a vowel too, in English?

And one more thing, thanx for your help

Last edited by Rose-Red (2006-11-12 07:13:52)

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## #4 2006-11-12 07:16:32

luca-deltodesco
Member
Registered: 2006-05-05
Posts: 1,470

### Re: Discrete maths - characteristic functions

Rose-Red wrote:

is letter "y" a vowel too, in English?

in english, y is both a vowel, and a consonant depending upon the word.

in words like hymn, the y is a vowel, but in words like beyond, y is a consonant

The Beginning Of All Things To End.
The End Of All Things To Come.

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## #5 2006-11-12 07:27:18

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: Discrete maths - characteristic functions

Y is always a consonant, it's just that there can be some words that contain y and no vowels. That doesn't suddenly turn y into a vowel though.

Why did the vector cross the road?
It wanted to be normal.

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## #6 2006-11-12 07:46:04

luca-deltodesco
Member
Registered: 2006-05-05
Posts: 1,470

### Re: Discrete maths - characteristic functions

mathsyperson wrote:

Y is always a consonant, it's just that there can be some words that contain y and no vowels. That doesn't suddenly turn y into a vowel though.

actually, according to the oxford, that is not true.

The Beginning Of All Things To End.
The End Of All Things To Come.

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## #7 2006-11-12 08:08:33

Rose-Red
Member
Registered: 2006-01-05
Posts: 19

### Re: Discrete maths - characteristic functions

well that's a controversial topic I started. In any case, I don't care anymore cause it doesn't change anything in my task.

thanx guys

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## #8 2006-11-12 08:08:47

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

### Re: Discrete maths - characteristic functions

mathsyperson wrote:

Y is always a consonant, it's just that there can be some words that contain y and no vowels. That doesn't suddenly turn y into a vowel though.

Why?

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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## #9 2006-11-12 08:20:20

luca-deltodesco
Member
Registered: 2006-05-05
Posts: 1,470

### Re: Discrete maths - characteristic functions

Ricky wrote:
mathsyperson wrote:

Y is always a consonant, it's just that there can be some words that contain y and no vowels. That doesn't suddenly turn y into a vowel though.

Why?

yeh, also, you technically cant make a sound, without using a vowel, because the vowel sounds, are the sounds, the consonants are just the way youre tounge, teeth lips and everything change to modify the vowel sound, without the vowel sound theres nothing, so you cant have a word without vowels, it would be completely inaudiable

rant over.

The Beginning Of All Things To End.
The End Of All Things To Come.

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## #10 2006-11-12 08:58:07

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: Discrete maths - characteristic functions

Huh. I stand corrected. I didn't realise consonants and vowels were defined by sounds rather than letters. Another occasion when common sense turns out to be wrong.

Why did the vector cross the road?
It wanted to be normal.

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## #11 2006-11-12 09:43:48

MathsIsFun
Registered: 2005-01-21
Posts: 7,659

### Re: Discrete maths - characteristic functions

I was taught that there are only 5 vowels aeiou. And I have also heard people say that words like fly have no vowels.

Perhaps there is a distinction between phonetic vowels and letter vowels?

So I think "controversial subject" is where it stands.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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