Apollo
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 Feb 12 comment Cardinality of all lines on $\mathbb R^{2}$ which do not contain point $(x,y)\in l$ where $x, y \in \mathbb Q$ Yep, though Ma.H did mention that the upper bound was obvious, so I didn't elaborate. (Though never hurts to give the complete argument). Feb 12 comment Cardinal arithmetic: $b\ge x>1$ and $b^2=b$ implies $x^b=2^b$ It's the only answer, so as bad as it is... :-) (Maybe if I remove the dependence on AC I'll get a vote?) Feb 11 revised Cardinal arithmetic: $b\ge x>1$ and $b^2=b$ implies $x^b=2^b$ added 814 characters in body Feb 11 answered Cardinal arithmetic: $b\ge x>1$ and $b^2=b$ implies $x^b=2^b$ Feb 11 revised Cardinal arithmetic: $b\ge x>1$ and $b^2=b$ implies $x^b=2^b$ Texified and corrected problem with $x=1$. Feb 11 suggested approved edit on Cardinal arithmetic: $b\ge x>1$ and $b^2=b$ implies $x^b=2^b$ Feb 11 answered What is an efficient algorithm to compute modular exponentiation of stacked exponents? Feb 11 answered Fastest way to compute HCF of 2 numbers Feb 10 comment Cardinality of all lines on $\mathbb R^{2}$ which do not contain point $(x,y)\in l$ where $x, y \in \mathbb Q$ How many irrationals are there? (If there are $\aleph_0$ rationals and $2^{\aleph_0}$ total real numbers, then ...) There is one horizontal line for each irrational. This will give you a lower bound (since there are lots of non-horizontal lines that miss rational points) on the number of lines you are looking for. Feb 10 comment Stone-Cech compactification problem Yeah, and for general spaces, i guess the same argument should work (if one is okay with non-Hausdorff compactification.) Feb 10 answered Injective maps from $B^A$ to $(C^B)^{C^A}$ Feb 10 answered Cardinality of all lines on $\mathbb R^{2}$ which do not contain point $(x,y)\in l$ where $x, y \in \mathbb Q$ Feb 10 answered Stone-Cech compactification problem Feb 9 awarded Revival Feb 9 answered Alexandroff compactification question Feb 9 awarded Mortarboard Feb 8 revised Cardinality of $P(\mathbb{R})$ and $P(P(\mathbb{R}))$ added 126 characters in body Feb 8 answered Cardinality of $P(\mathbb{R})$ and $P(P(\mathbb{R}))$ Feb 8 awarded Necromancer Feb 8 comment Size of the closure of a set Yes, I wouldn't be surprised if there weren't an independence result here, something like $\text{MA}+2^{\aleph_0}=\aleph_2$ implying that every separable, sequentially-compact, (+compact?) space is $\leq\aleph_2$. For example, there's the result that if $\mathfrak{c}\leq\aleph_2$ then every compact, sequentially-compact space is pseudo-radial, etc.