Does Infinity Belong to a Set? Understanding the Concept of Infinity

In summary, infinity is a concept in mathematics that represents a quantity or value that is greater than any number. It is not considered a number and is not included in the set of real numbers. Infinity cannot be reached or measured and there are different sizes of infinity in mathematics.
  • #1
johann1301
217
1
Is infinity part of any set?
 
Physics news on Phys.org
  • #2
johann, I am locking this thread because you are making many different threads with just one question. Can you please make one thread containing all of your questions? Furthermore, can you also give the necessary background information such as why you ask this, what the relevant definitions are and what your thoughts are on the matter.
 
  • Like
Likes 1 person

1. What is infinity?

Infinity is a concept in mathematics that represents a quantity or value that is greater than any number. It is often denoted by the symbol ∞.

2. Is infinity a number?

No, infinity is not considered a number in mathematics. It is a concept or idea that represents a value larger than any number.

3. Is infinity part of the real numbers?

No, infinity is not included in the set of real numbers. The real numbers include all rational and irrational numbers, but infinity is not a number and therefore not part of this set.

4. Can infinity be reached or measured?

No, infinity cannot be reached or measured in the same way that we measure finite quantities. It is a concept that represents a value that is always larger than any number, so it cannot be reached or measured in the traditional sense.

5. Are there different sizes of infinity?

Yes, there are different sizes of infinity in mathematics. For example, the set of all counting numbers (1, 2, 3, etc.) has a smaller infinity than the set of all real numbers, as there are an infinite number of real numbers between any two counting numbers.

Similar threads

  • Set Theory, Logic, Probability, Statistics
Replies
1
Views
696
  • Set Theory, Logic, Probability, Statistics
Replies
1
Views
1K
  • Set Theory, Logic, Probability, Statistics
Replies
14
Views
1K
Replies
7
Views
537
  • Set Theory, Logic, Probability, Statistics
Replies
13
Views
962
  • Special and General Relativity
Replies
30
Views
6K
  • General Math
2
Replies
40
Views
3K
Replies
2
Views
131
  • Set Theory, Logic, Probability, Statistics
Replies
1
Views
750
  • Set Theory, Logic, Probability, Statistics
Replies
6
Views
1K
Back
Top