The class of all ordinals. The class of cardinals is embedded within it (if AC holds) since one identifies a cardinal with the smallest ordinal such that the set of all smaller ordinals has that cardinality. ($\aleph_0$ is the cardinality of the set of all finite ordinals, $\aleph_1$ is the cardinality of the set of all countable ordinals, etc. The $\aleph_\omega$ cardinality of the set of all ordinals whose cardinality is $\aleph_n$ for some finite $n$. ($\omega$ is the ordinal that gets identified with $\aleph_0$ in the aforementioned identification) $\aleph_{\omega+1}$ is the set of all ordinals of cardinality $\aleph_\omega$, and so on. $\aleph_\omega$ is the smallest cardinal greater than $\aleph_0$ that is known not to be equal to $2^{\aleph_0}$.)

But if grading is only based on "intricacy", maybe the class of all sets, conventionally denoted "V" because it looks like the letter V (?) might be in first place. Some people have tried to embed all of mathematics within this thing.

Later edit: The "\aleph"s and the "\omega"s are failing to get rendered when I view this thing. Look at the code and you'll see them.

The class of all ordinals. The class of cardinals is embedded within it (if AC holds) since one identifies a cardinal with the smallest ordinal such that the set of all smaller ordinals has that cardinality. ($\aleph_0$ is the cardinality of the set of all finite ordinals, $\aleph_1$ is the cardinality of the set of all countable ordinals, etc.   $\aleph_\omega$ is the cardinality of the set of all ordinals whose cardinality is $\aleph_n$ for some finite $n$. ($\omega$ is the ordinal that gets identified with $\aleph_0$ in the aforementioned identification) $\aleph_{\omega+1}$ is the set of all ordinals of cardinality $\aleph_\omega$, and so on. $\aleph_\omega$ is the smallest cardinal greater than $\aleph_0$ that is known not to be equal to $2^{\aleph_0}$.)

But if grading is only based on "intricacy", maybe the class of all sets, conventionally denoted "V" because it looks like the letter V (?) might be in first place. Some people have tried to embed all of mathematics within this thing.

Later edit: The "\aleph"s and the "\omega"s are failing to get rendered when I view this thing. Look at the code and you'll see them.

The class of all ordinals. The class of cardinals is embedded within it (if AC holds) since one identifies a cardinal with the smallest ordinal such that the set of all smaller ordinals has that cardinality. ($\aleph_0$ is the cardinality of the set of all finite ordinals, $\aleph_1$ is the cardinality of the set of all countable ordinals, etc. The $\aleph_\omega$ cardinality of the set of all ordinals whose cardinality is $\aleph_n$ for some finite $n$. ($\omega$ is the ordinal that gets identified with $\aleph_0$ in the aforementioned identification) $\aleph_{\omega+1}$ is the set of all ordinals of cardinality $\aleph_\omega$, and so on. $\aleph_\omega$ is the smallest cardinal greater than $\aleph__0$ that is known not to be equal to $2^{\aleph_0}$.)

But if grading is only based on "intricacy", maybe the class of all sets, conventionally denoted "V" because it looks like the letter V (?) might be in first place. Some people have tried to embed all of mathematics within this thing.

Later edit: The "\aleph"s and the "\omega"s are failing to get rendered when I view this thing. Look at the code and you'll see them.

The class of all ordinals. The class of cardinals is embedded within it (if AC holds) since one identifies a cardinal with the smallest ordinal such that the set of all smaller ordinals has that cardinality. ($\aleph_0$ is the cardinality of the set of all finite ordinals, $\aleph_1$ is the cardinality of the set of all countable ordinals, etc. The $\aleph_\omega$ cardinality of the set of all ordinals whose cardinality is $\aleph_n$ for some finite $n$. ($\omega$ is the ordinal that gets identified with $\aleph_0$ in the aforementioned identification) $\aleph_{\omega+1}$ is the set of all ordinals of cardinality $\aleph_\omega$, and so on. $\aleph_\omega$ is the smallest cardinal greater than $\aleph_0$ that is known not to be equal to $2^{\aleph_0}$.)

But if grading is only based on "intricacy", maybe the class of all sets, conventionally denoted "V" because it looks like the letter V (?) might be in first place. Some people have tried to embed all of mathematics within this thing.

Later edit: The "\aleph"s and the "\omega"s are failing to get rendered when I view this thing. Look at the code and you'll see them.