Is infinity truly infinite if it has something else in it?

In summary, the concept of infinity does not change based on the presence of other objects within it. An infinite set can still contain subsets that are also infinite. This idea is seen in examples such as Hilbert's hotel, where an infinite number of guests can be added to an infinite number of rooms without changing the overall infinity of the set. In the context of space or spacetime, the concept of infinity does not change even if there are regions with boundaries or places without certain elements. Therefore, the volume of water can still be considered infinite even if there are rocks within it or places without water.
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ddjj77
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Is infinity truly infinite if it has something else in it?
Put differently, say there's an infinite volume of water that has some rocks in it, is the volume of water truly infinite? Though there's a place where there's no water?
 
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  • #2
Yes, a subset of an infinite set can also be infinite. For example, there is an infinite number of odd numbers even though you have to remove another infinite set (the even numbers) from the natural numbers to get the odd numbers. This leads to things such as Hilbert's hotel.
 
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What does "truly infinite" mean?

Certainly you can have infinite regions with boundaries - an infinite volume minus a finite volume is still infinite. I presume, since you're posting this in cosmology, that you're thinking of space or spacetime. This doesn't have any holes in it anyway, so far as we are aware.
 
  • #4
Then when I use the term "infinite volume of water", this shouldn't mean there's water everywhere. Got it.
 
  • #5
ddjj77 said:
Is infinity truly infinite if it has something else in it?
Put differently, say there's an infinite volume of water that has some rocks in it, is the volume of water truly infinite? Though there's a place where there's no water?
Infinity is a mathematical concept. If you can put rocks in it, you speak about something which exists within the universe, and then - in case it should be infinite - all rocks are already in it.
 
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1. What is infinity?

Infinity is a concept in mathematics and philosophy that refers to something that has no limit or end. It can be thought of as a concept of endlessness or boundlessness.

2. How is infinity defined?

Infinity is often defined as the idea of something that is larger than any real or natural number. It is an abstract concept that cannot be measured or counted.

3. Is infinity truly infinite?

Yes, according to mathematical and philosophical theories, infinity is considered to be truly infinite. It is a limitless concept that cannot be contained or defined by any specific value or quantity.

4. Can something else exist within infinity?

Yes, it is possible for something else to exist within infinity. For example, in the concept of the multiverse, it is believed that there are infinite parallel universes within infinity.

5. How does the concept of infinity relate to the universe?

The concept of infinity is often used to describe the vastness and endlessness of the universe. It is believed that the universe is infinite and constantly expanding, with no boundary or end.

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