Math Is Fun Forum
You are not logged in.
- Topics: Active | Unanswered
#1 2007-08-14 00:56:17
- wasee
- Member
- Registered: 2007-08-12
- Posts: 2
Empty Set
We say that a set is a collection of well-defined distinct things. Why ,then ,is an empty set a set?
Offline
#2 2007-08-14 01:23:49
- mathsyperson
- Moderator
- Registered: 2005-06-22
- Posts: 4,900
Re: Empty Set
Because it's still a set, it just happens to not contain anything. Emptying a box doesn't make it disappear.
Why did the vector cross the road?
It wanted to be normal.
Offline
#3 2007-08-14 19:02:22
- wasee
- Member
- Registered: 2007-08-12
- Posts: 2
Re: Empty Set
Well ,the point is ,does it not contradict the definition?
Offline
#4 2007-08-14 19:13:23
- MathsIsFun
- Administrator
- Registered: 2005-01-21
- Posts: 7,713
Re: Empty Set
Can you have zero things? I think so.
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman
Offline
#5 2007-08-15 01:13:43
- Ricky
- Moderator
- Registered: 2005-12-04
- Posts: 3,791
Re: Empty Set
Nothing is a collection of distinct things. I don't see how it does.
"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..."
Offline
#6 2007-08-15 04:11:48
- HallsofIvy
- Guest
Re: Empty Set
You just said it didn't you? "Nothing" is a set of distinct things and that describes the empty set very well!
#7 2007-08-15 04:27:51
- Ricky
- Moderator
- Registered: 2005-12-04
- Posts: 3,791
Re: Empty Set
If you're referring to my post, it was supposed to read, "I don't see how it doesn't fit your definition." But something got cutoff. Either a computer glitch or PEBCAK. *shrug*
"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..."
Offline
#8 2007-08-16 00:48:22
- George,Y
- Member
- Registered: 2006-03-12
- Posts: 1,379
Re: Empty Set
I don't have anything= I have nothing.
The latter setence uses the concept of vanity(nothing) although the same meaning.
wasee you know what? Your idea is quite the same as that of the Ancient Roman people.
How to record not having any amount? Simply not writing down anything.
So they don't have 0, and they only have numbers that stands for some amount real, concrete.
However, the Ancient Indians, had a different idea.
Not any = 0. 0 means vanity. Vanity has something to do with the Ancient Indian philosophy. The concept of vanity, not any thing, is a critical part in the philosophy.
So they are the creators of the 0.
And 0 simply means no value.
Looks like abundant rubbish.
But when you have 23-3, you will realize the very usage of it. It can be used with other concrete values together to create a simpler expression.
So when you ask about where an empty set is useful,
I can tell you it can have relationship with other sets, like A and Empty is Empty, A or Empty is A, etc.
X'(y-Xβ)=0
Offline
#9 2007-08-16 01:03:46
- JaneFairfax
- Member
- Registered: 2007-02-23
- Posts: 6,868
Re: Empty Set
Reminds me of the catchphrase that was once used by the manufacturers of Anadin headache tablets. Nothing Works Faster Than Anadin, they said, full of vanity.
All right, some smart guy then said. From now on, when I have a headache, I will take nothing, because nothing works faster than Anadin.
As a result, Anadin have since changed their catchphrase to To Beat Pain Fast. 
Last edited by JaneFairfax (2007-08-16 01:05:27)
Offline
#10 2007-08-16 10:12:46
- MathsIsFun
- Administrator
- Registered: 2005-01-21
- Posts: 7,713
Re: Empty Set
LOL!
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman
Offline