Josh Infiesto
Reputation
730
Top tag
Next privilege 1,000 Rep.
Create tags
 Apr15 accepted Expressing a line as a linear combination of two points on the line. Apr14 comment Expressing a line as a linear combination of two points on the line. That was my intuition as well. But it didn't really satisfy me as I wouldn't have thought "Oh that's obvious" just from the intuition. But it makes sense retrospectively I suppose. Apr14 comment Expressing a line as a linear combination of two points on the line. Yes. That is correct. Apr14 revised Is the Godeaux surface irrational? spelling and grammar Apr14 suggested approved edit on Is the Godeaux surface irrational? Apr14 asked Expressing a line as a linear combination of two points on the line. Apr14 awarded Necromancer Jan15 awarded Notable Question Jan6 accepted Confusion concerning Cantor's theorem. Jan6 comment Confusion concerning Cantor's theorem. I'm aware of that, which is why I specified that the power set is a subset of the described set. I should have specified that I was considering the power set to be the set of equivalence classes on the larger set given the appropriate equivalence relation. But, the first reason you gave mostly clears it up for me. Thanks. Jan6 comment Confusion concerning Cantor's theorem. I edited my question to hopefully be more clear. Jan6 revised Confusion concerning Cantor's theorem. added 27 characters in body Jan6 asked Confusion concerning Cantor's theorem. Oct30 accepted Confusion about least upper bound property of reals constructed as Dedekind Cuts. Oct30 comment Confusion about least upper bound property of reals constructed as Dedekind Cuts. Not at all, this was enlightening. I think I just need to ponder infinite sets for a bit. Oct30 comment Confusion about least upper bound property of reals constructed as Dedekind Cuts. I'm fine with statements and quantifiers. I think I'm being freaked out by the fact that left part of every successive cut in $\mathcal{C}$ is a subset of the left part of the next cut, so I guess, to use your example, my intuition for cuts looks more like $A_1 = \{1\}$ and $A_2 = \{1, 2\}$ for which the above statements do not hold for $A$, $A_1$ and $A_2$. Oct30 comment Confusion about least upper bound property of reals constructed as Dedekind Cuts. It's confusing to me that both the above statements can be true. Do you know a resource where I can read more about this? Oct30 comment Confusion about least upper bound property of reals constructed as Dedekind Cuts. Alright, I think I mostly get it. Can you explain what it is about infinity that makes this so? In my head, this still seems somewhat paradoxical. I guess my reasoning is that since every $H_n \subset H$ $H > H_n$ for all $H$. On the other hand though, since $H$ is the union of all $H_n$, there is no element in $H$ that does not appear in some $H_n$, which is what's bugging me still. Infinity makes my head hurt. Oct30 asked Confusion about least upper bound property of reals constructed as Dedekind Cuts. Oct4 awarded Yearling