There is no "greatest" infinity

# Thread: There is no "greatest" infinity

1. ## There is no "greatest" infinity

According to https://en.wikipedia.org/wiki/Cantor%27s_paradox, there's no such thing as an infinite set that is larger than every other infinite set. I understand the idea behind it, but the notion sounds ridiculous to me. Surely there has to be something that is absolutely and totally infinite?

2. ## Re: There is no "greatest" infinity

hmm did you read the 2nd paragraph of the page you linked?

the paradox applies specifically to set theory because of the way sets and the like are defined. If you try to declare there is some set that contains all other sets - well that's cool and all but i can just make the power set of that set and bam i have a bigger one. hence there's no way you could ever have a "largest" set.

this doesn't necessarily apply to other abstract concepts of infinity, although in pretty much any case where your infinity has some arbitrary rules or bounds to it then we could find a way to break those bounds. Meanwhile a "pure infinity" with no limitations would be a pretty useless concept since there'd be no way to interact with it.

3. ## Re: There is no "greatest" infinity

Originally Posted by DJarJar
hmm did you read the 2nd paragraph of the page you linked?

the paradox applies specifically to set theory because of the way sets and the like are defined. If you try to declare there is some set that contains all other sets - well that's cool and all but i can just make the power set of that set and bam i have a bigger one. hence there's no way you could ever have a "largest" set.

this doesn't necessarily apply to other abstract concepts of infinity, although in pretty much any case where your infinity has some arbitrary rules or bounds to it then we could find a way to break those bounds. Meanwhile a "pure infinity" with no limitations would be a pretty useless concept since there'd be no way to interact with it.
It seems to me the definition of infinity in math is slightly different than in normal parlance. As far as I can tell, something is infinite if it "never ends" if you try to list every single element in that "it". But normally when we talk about infinity we mean some abstract thing that is very large in size and which includes "everything" else.

4. ## Re: There is no "greatest" infinity

Let's not conflate mathematical definitions with whatever definitions we feel comfortable with, because this is the biggest source of definitional fuckery that goes nowhere. These definitions in math are constructed from the ground up and have no notion of what infinity is. As a result of multiple theorems and proofs, we can show that different kinds of infinities exist, and while some are larger than others, no infinity can be smaller than the set of natural numbers.

The definition of infinite in math is something that is not finite. It's weird putting it that way but it really is; infinity is defined by the not finite state of something. In real analysis this means that there is no bound to a set. Saying that something "never ends" is reductive because depending on how we construct that "never ending" collection we will arrive that the place where there are infinities of different sizes, and as Cantor's paradox comes from the fact that there is no such thing as a "biggest" set, and if we were to assume such a set exists that has infinite cardinality then it would be the "biggest infinity", holding other infinities inside it. When people say infinity is an idea, it is; depending on how you construct it and use it.

Normal parlance can suck it because it makes no sense outside of general conversation and metaphors

5. ## Re: There is no "greatest" infinity

Originally Posted by Plotato
Let's not conflate mathematical definitions with whatever definitions we feel comfortable with, because this is the biggest source of definitional fuckery that goes nowhere. These definitions in math are constructed from the ground up and have no notion of what infinity is. As a result of multiple theorems and proofs, we can show that different kinds of infinities exist, and while some are larger than others, no infinity can be smaller than the set of natural numbers.

The definition of infinite in math is something that is not finite. It's weird putting it that way but it really is; infinity is defined by the not finite state of something. In real analysis this means that there is no bound to a set. Saying that something "never ends" is reductive because depending on how we construct that "never ending" collection we will arrive that the place where there are infinities of different sizes, and as Cantor's paradox comes from the fact that there is no such thing as a "biggest" set, and if we were to assume such a set exists that has infinite cardinality then it would be the "biggest infinity", holding other infinities inside it. When people say infinity is an idea, it is; depending on how you construct it and use it.

Normal parlance can suck it because it makes no sense outside of general conversation and metaphors
I disagree, if it "makes no sense" outside of normal parlance, then it is mathematical definitions that do not make sense. People came up with these definitions according to an intuitive understanding of what infinity is. Math is intended to represent some "real" notion, it's not just made up nonsense.

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