Find a set A (subset of R,set of real numbers) and an element a of R

In summary, we are looking for a set A, a subset of the real numbers, and an element a of the real numbers such that there is no bijection from a+A to A. Examples of such sets include finite sets like A= {1, 2, 3} and a= 0, as well as the empty set A= {} and any real number a.
  • #1
julia89
6
0
Find a set A (subset of R,set of real numbers) and an element a of R
such that there is no bijecton from a+A(we add a to the set A)to A.

I can't find a good example. Can someone help
Are we done if we choose the empty set? (And is the empty set a subset of R?)

Thank you
 
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  • #2
?? Any finite set will do. Take A= {1, 2, 3} and a= 0. Then A has 3 members while A+ a has 4. There cannot be a bijection from one to the other.

Yes, the empty set is a subset of R (it is a subset of any set). Choosing A= {} and a any real number so that A+ a= {a} will also work.
 

FAQ: Find a set A (subset of R,set of real numbers) and an element a of R

1. What is a subset of real numbers?

A subset of real numbers is a set that contains a portion of the real numbers. This means that all the elements in the subset are also elements of the larger set of real numbers.

2. How do I find a subset of real numbers?

To find a subset of real numbers, you can first determine the specific criteria or characteristics that you want the subset to have. Then, you can use this criteria to select the elements from the larger set of real numbers to create the subset.

3. Can a subset of real numbers contain any type of number?

Yes, a subset of real numbers can contain any type of number, including integers, decimals, and irrational numbers. As long as the numbers meet the criteria for the subset, they can be included.

4. What is an element of a set of real numbers?

An element of a set of real numbers is a single number that is a part of the set. It can be any type of number, as long as it is a real number.

5. How do I know if an element is a part of a subset of real numbers?

To determine if an element is a part of a subset of real numbers, you can check if the element meets the criteria or characteristics that were used to create the subset. If it does, then it is an element of the subset.

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