Understanding Null Sets: Exploring the Concept of Measure Zero

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In summary, a null set is a set that contains nothing and has a cardinality of zero. It is often used to differentiate between "something" and "nothing". It is also known as an empty set and is unique. In mathematics, a null set is one that has a measure of zero, and can be demonstrated through examples such as the set of rational numbers.
  • #1
mooberrymarz
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Wot exactly is a null set? i don't understand it. if anyone could explain that wuld be wikid. :cool:
 
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  • #2
it would depend on the context, but it is, generically, something that is zero.
 
  • #3
It exists to make difference between "something" and "nothing". A set that contains something is like something and the null set is nothing (contains nothing)
 
  • #4
No, that is not necessarily true. A null set, could be, as I suspect it will be in this case, a set of measure zero.
 
  • #5
ok..maybe my english is not good enough.. what is that called: ø?
 
  • #6
isn't it a null set? or an empy set?
 
  • #7
that is the empty set. It is a null set in the sense that its cardinality is zero.
 
  • #8
is there any other set, whiches cardinality is zero exept the empty set?
I don't think so
 
  • #9
No, it, the empty set, is unique. But that doesnt' have any bearing on what a null set is until we see what situation we are dealing with.
 
  • #10
For example.. the set of rationals and irrationals. rationals are a null set and wot bout irrationals?? Matt could u explain in dummy maths why rationals are a null set?
 
  • #11
As I thought, a null set is one that has measure zero. Example: and countable subset of R (Eg the rationals): let x_i be an enumeration of the set, round each point x_i consider the interval e/2^i, then the measure of the set is less than the sum over i of e^2^i = e. e was arbitrary hence it has measure zero.
 

FAQ: Understanding Null Sets: Exploring the Concept of Measure Zero

What is a null set?

A null set is a mathematical concept that represents a set with no elements. It is often denoted by the symbol ∅ or {}.

How is a null set different from an empty set?

A null set is a specific type of empty set that has been defined in mathematics. It differs from an empty set in that it specifically has no elements, whereas an empty set can still contain other sets or objects.

What is the cardinality of a null set?

The cardinality, or size, of a null set is zero. This is because it contains no elements.

What is the purpose of a null set in mathematics?

A null set is often used in mathematical proofs and definitions to represent the absence of a specific set or element. It can also be used to represent impossible or undefined situations.

Can a null set contain another set?

No, a null set cannot contain any other sets or elements. It is defined as having no elements, so it cannot contain anything else.

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