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Apr
15
accepted Expressing a line as a linear combination of two points on the line.
Apr
14
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.
Apr
14
comment Expressing a line as a linear combination of two points on the line.
Yes. That is correct.
Apr
14
revised Is the Godeaux surface irrational?
spelling and grammar
Apr
14
suggested approved edit on Is the Godeaux surface irrational?
Apr
14
asked Expressing a line as a linear combination of two points on the line.
Apr
14
awarded  Necromancer
Jan
15
awarded  Notable Question
Jan
6
accepted Confusion concerning Cantor's theorem.
Jan
6
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.
Jan
6
comment Confusion concerning Cantor's theorem.
I edited my question to hopefully be more clear.
Jan
6
revised Confusion concerning Cantor's theorem.
added 27 characters in body
Jan
6
asked Confusion concerning Cantor's theorem.
Oct
30
accepted Confusion about least upper bound property of reals constructed as Dedekind Cuts.
Oct
30
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.
Oct
30
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 $A_2$.
Oct
30
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?
Oct
30
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.
Oct
30
asked Confusion about least upper bound property of reals constructed as Dedekind Cuts.
Oct
4
awarded  Yearling