# Are the Sets {r, -r, 0} and {-r, r, 0} Identical?

In summary: Thank you for the explanation! In summary, this sets are the same because they have the same elements in the same order.

## Homework Statement

Is the set (r,-r,0) the same as the set (-r,r,0)

Sorry I need to know the answer to this right now, somebody in class confused me and I can't talk to my teacher right now.

My answer: yes it is the same set. Can anyone just give me a quick yes/no?

## The Attempt at a Solution

I have to brake for a car in front of me, so I can't answer 'it depends' right now !

good luck with your test !

member 587159

## Homework Statement

Is the set (r,-r,0) the same as the set (-r,r,0)

Sorry I need to know the answer to this right now, somebody in class confused me and I can't talk to my teacher right now.

My answer: yes it is the same set. Can anyone just give me a quick yes/no?

## The Attempt at a Solution

Yes, as sets they are the same. Order doesn't matter here.

I wasn't really in a car, but safely behind my desktop. Just didn't want to interfere in a testing situation

If the order of elements in a set matters, we call it a sequence. (You need a sequence of instructions when asking directions; with a set you wouldn't know what to do first)

A set is a collection. Two collections are the same if they contain the same elements. Yours do

## Homework Statement

Is the set (r,-r,0) the same as the set (-r,r,0)

Sorry I need to know the answer to this right now, somebody in class confused me and I can't talk to my teacher right now.

My answer: yes it is the same set. Can anyone just give me a quick yes/no?

## The Attempt at a Solution

Your notation is poor: in Mathematics, we almost always denote sets using curly brackets, like this: ##\{ r, -r,0 \}##, and in that case, order does not matter: ##\{ r,-r,0 \} = \{ r,-r,0 \} = \{ r,0,-r \} = \{ -r,0,r \} = \{ 0,r,-r \} = \{ 0,-r,r \}. ## Other types of brackets like ( , ) , [ , ] or < , > denote objects like lists, vectors, arrays, sequences, etc., and for all of them order is crucial.

FactChecker

## 1. What is the difference between two sets?

The main difference between two sets is that they contain different elements. Sets are mathematical structures that contain distinct objects, and the elements within a set do not have a specific order or sequence.

## 2. How are sets represented in mathematics?

In mathematics, sets are typically represented using curly braces { } and listing the elements within the set. For example: Set A = {1, 2, 3}.

## 3. What is the cardinality of a set?

The cardinality of a set refers to the number of elements within the set. This can be determined by counting the number of objects in the set or using mathematical operations such as the "size" function.

## 4. Can two sets have the same elements but different cardinalities?

No, if two sets have the same elements, they have the same cardinality. Even if the elements are listed in a different order, as long as the elements are the same, the sets have the same cardinality.

## 5. How are sets related to other mathematical concepts?

Sets are fundamental to many branches of mathematics including algebra, geometry, and calculus. They are used to define and solve problems in these areas, and are essential for understanding mathematical functions and relationships between quantities.

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