What's the cardinality of the infinity introduced in Riemann sphere model? In the Riemann sphere model, people extend the complex plane with a point at infinity: $\mathbb {C} \cup \{\infty \}$ and claim this expression: $\frac{1}{0}=\infty$.
I'm confused with what is this $\infty$. Is it a member of $\{\aleph_n\}$ numbers?
When we study infinities, we usually discuss cardinality. Does this $\infty$ corresponds to something's cardinality?


Does it has a cardinality?

No. The $\infty$ there doesn't represent a particular set (though you might have to encode it as a set if you're using set theory as your foundation), nor the cardinality of a particular set.

What's the property of this infinity?

The properties are discussed throughout the English Wikipedia article for "Riemann sphere". Is there a particular property you have a question about?
