Understanding Infinity: Is Every Number Included?

  • I
  • Thread starter DaMeekie
  • Start date
  • Tags
    Infinity
In summary, there are infinitely many numbers between any two real numbers, and infinity does not necessarily include every number. However, in equations, infinity and real numbers can be used together to create differences. The equation ∞14 + ∞18 = ∞32 does not hold true. For more information on infinity, please refer to the Math FAQ provided.
  • #1
DaMeekie
6
0
Assuming that this next statement is correct, that there are an infinite amount of numbers between the numbers "1 and 2", and another, different set of infinite numbers between "2 and 3".
All I'm trying to take out of this is that infinity doesn't necessarily mean every number, but at the same time it could.
If this is true then you could have infinity in an equation but also have real numbers to create differences in them because they are constants.

∞14 + ∞18 = ∞32

I'm sure this could go much further, but I'm not even sure if this is already something used. If you have any information, even a link would be nice.
Much Thanks
-DaMeek
 
Mathematics news on Phys.org
  • #2
DaMeekie said:
Assuming that this next statement is correct, that there are an infinite amount of numbers between the numbers "1 and 2", and another, different set of infinite numbers between "2 and 3".
A better way to say this is that there are an infinite number of numbers between 1 and 2, as well as between 2 and 3. In fact, between any two real numbers, there are an infinite number of numbers
DaMeekie said:
All I'm trying to take out of this is that infinity doesn't necessarily mean every number, but at the same time it could.
If this is true then you could have infinity in an equation but also have real numbers to create differences in them because they are constants.

∞14 + ∞18 = ∞32
That's not the way it works. We have a Math FAQ that discusses infinity - https://www.physicsforums.com/insights/questions-about-infinity/
DaMeekie said:
I'm sure this could go much further, but I'm not even sure if this is already something used. If you have any information, even a link would be nice.
Much Thanks
-DaMeek
 
Last edited by a moderator:

What is infinity?

Infinity is a concept that describes something that has no end or limit. It is often used in mathematics and philosophy to represent a quantity or value that is larger or smaller than any number that can be expressed.

Are there different types of infinity?

Yes, there are different types of infinity. The most commonly known types are countable infinity and uncountable infinity. Countable infinity refers to a set of items that can be counted, such as the natural numbers. Uncountable infinity refers to a set of items that cannot be counted, such as the real numbers.

How do we compare different infinities?

Different infinities can be compared using cardinality, which is a way of measuring the size of a set. If two sets have the same cardinality, they are considered to have the same size. For example, the set of natural numbers and the set of even numbers have the same cardinality, even though one is a subset of the other.

What is the difference between potential and actual infinity?

Potential infinity refers to a process that can continue indefinitely, whereas actual infinity refers to a completed set that contains an infinite number of items. For example, the process of counting can continue indefinitely, but the set of all natural numbers is an actual infinity.

Are there practical applications of infinity?

Yes, infinity has many practical applications in mathematics, physics, and computer science. For example, calculus uses the concept of infinity to solve problems related to limits and infinite series. Infinity is also used in physics to describe the behavior of the universe, and in computer science to represent infinite data structures and algorithms.

Similar threads

B Is one out of infinity different from zero?
    • General Math
Replies
31
Views
1K
B Arithmetic mean of an infinite number of points?
    • General Math
Replies
20
Views
1K
I Expressing any given point on plane with one unique number
    • General Math
Replies
4
Views
617
B My argument why Hilbert's Hotel is not a veridical Paradox
    • General Math
Replies
8
Views
1K
B Hilbert's Hotel: new Guest arrives (Infinite number of Guests)
    • General Math
2
Replies
69
Views
5K
I Integrity of matter / space and time
    • Other Physics Topics
Replies
13
Views
3K
I What is the role of geometry and dimensional operations?
    • General Math
Replies
3
Views
265
Does Infinity Exist in the Real Universe?
    • General Math
Replies
4
Views
1K
I Future null infinity confusion
    • Special and General Relativity
Replies
30
Views
6K
A Choices of Axiomatic and Number Systems / Sets and Alternatives
    • General Math
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top