In mathematics, there can be infinite sets in topological space. In one sense, this shows that infinity exists. However, infinity is not itself a number, but a relationship between hypothetical numbers that cannot be finished being counted to. So a mathematical equation, or rubric, can demonstrate infinity, but still does not satisfy the requirements necessary for there to be an infinite amount of actual physical objects. The very question "Is there an infinite amount of" or "Is there an infinite number of" x items actually in existance seems flawed because there cannot be an "infinite number". For there to be an infinite number of things, infinity would have to be a number. However, there is no number itself actually equal to infinity, so infinity is not a number.

I agree that the math behind infinite sets is logical and correct. The problem I see is that though a set of numbers can converge on infinity, the fact remains that it never "reaches" infinity. In this way, the universe, or all of existence, can converge to infinity, but never reach it. Existence can be said to have no limit, but that's not actually the same thing as being infinite.

Equations containing numbers and symbols are good representations of objects, but you can't actually have your equation truly represent infinity in numbers. You demonstrate that the relationship is infinite, for example there is an infinite relationship between even and odd numbers, but you can never actually write down and show an infinite amount of numbers themselves. Relationships can be infinite sets, but it seems the number of objects that exist cannot.

This is why I put "reaches" in quotations. Its absurd to think that you can "approach" something that is indefinite. I do agree that a universe can contain elements that can be modeled with infinities. Infinities are even different "sizes" in different sets. This is in relationships, which can only be represented by numbers, but do not actually equal a total number. You can never write down every number in an infinite set. Still there is such a "thing" as infinity. A relationship doesn't necessarily have to have a set number of actual objects, only infinite relationship. "Relationship" is not a discrete object, so this is why a set can be infinite.

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However, a group of objects behaves differently than a set in that there is a number of objects. Each object is discrete, or else it would not qualify as being an object. The relationship between any set of these objects might be infinite, but the number of the objects themselves can never "equal" infinity because in order to equal it, it would have to be a definite number

I said they "might" be infinite, not that any set of objects "do" have an infinite relationship.

{1, 2, 3 ... } is not a number, its a description of a relationship or property of "ongoingness", but has no actual, ultimate, or specific value. No specific one number is equal to it.

The point isn't what term to use, and the point isn't whether or not you can demonstrate infinity, or infinite sets with math. Using the term "specific value" is perfectly valid. I could just as easily say "specific number" or "specific ammount", the term is irrelevant. The point is that though you can demonstrate infinity through math, you can never have infinite actual objects.

The "infinite relationship" I am refering to is the characteristic of the cardinal set such that 1 is related to 2 the same way that 2 is related to 3 and the same relationship is true of all integers. The only way you demonstrate infinity is by this relationship. You don't actually have a number "infinity", you only have an infinite relationship, otherwise, the statement that the cardinal set is infinite would be impossible.

No matter how much you can demonstrate this, or how many terms you come up with to define it, the very simple fact that you still never have a number equal to infinity remains. Its not a number, so there can't be a number of things equaling it. So there aren't infinite things.

I disagree that anything about the nature of the infinite is obvious, wrong or right.

In cosmology, the density of a universe dictates, in part, the radius of the curvature of that universe, not the number of universes. Again, being infinite is a characteristic that exists in some contexts.

A number cannot have the characteristic of being infinite. Infinity is not a number. So you can't say you have "infinitely many universes" because that is quite literally another way of saying "an infinite number of universes", which is a contradition in terms.

You can indeed model some characteristics with infinities including some characteristics of the universe itself. The number objects that exist is not one of these.

You can't have "infinite many" or "infinite amount" because "many" and "ammount" imply a number.

I was wondering when someone was going to ask this question. No. The lexicon does not govern reality, it is the other way around. Our language is part of reality, and a way to describe realtiy. The word "number" does not govern the characteristics of the universe, but is simply our way of communicating to one another that the object being refered to has the characterisitic of being a number.

If the configurations are infinite, then there are no configurations that are not.

If the configurations are infinite, you cannot have one less than infinity.