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 Dec9 awarded Notable Question Oct13 awarded Notable Question Sep24 awarded Autobiographer Aug19 awarded Popular Question Jul2 awarded Curious May16 awarded Popular Question Feb26 awarded Popular Question Nov26 awarded Popular Question Sep26 awarded Popular Question Sep17 accepted Let $C$ be a set of sets defined as follows, Sep17 comment Let $C$ be a set of sets defined as follows, Oh yeah, I'm really smart. So the elements of $C$ either have cardinality of 1 due to (1), 2 due to (2), or powers of 2 due to (3). Sep17 comment Let $C$ be a set of sets defined as follows, Ok good, because now it makes sense. So clearly there are no infinite sets in $C$ because for $S, T\in C$ $|\{S, T\}| = |S|+|T|$ and $|S\times T|=|S|*|T|$. But it's uncountable because there are infinitely many ways to combine elements of $C$ using either (2) or (3), right? I can't think of a way in which $C$ could be countable. Sep17 comment Let $C$ be a set of sets defined as follows, Oh okay that makes sense. But do we know anything other than constructions based on the empty set? Sep17 comment Let $C$ be a set of sets defined as follows, Thank you, that was part a) actually. I figured that out similarly to how you've done it. What I'm struggling with is understanding how ordered pairs can come into play. If we let $S=\{(a,b),(c,d)\}$ for example, we can have $\{S,\emptyset\}$, but how do I know that's in $C$? Sep17 asked Let $C$ be a set of sets defined as follows, Feb15 awarded Yearling Nov1 comment Aristotle's Axiom in Hyperbolic Geometry @Berci Yes, that is the Angle Unboundedness Axiom in Euclidean/Neutral geometry, but I need to figure out a way to prove that statement holds in Hyperbolic geometry. Nov1 asked Aristotle's Axiom in Hyperbolic Geometry Oct22 accepted Proving a function $f$ is continuous at a point $a$ Oct22 comment Proving a function $f$ is continuous at a point $a$ Okay, got it. Thank you very much!!