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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
Oct
3
accepted Help with this related rates problem.
Oct
3
comment Help with this related rates problem.
Thanks. I thought that this was the case, but also suspected I might be missing something as the rest have numeric solutions.
Oct
3
comment Help with this related rates problem.
As stated in the question, I am aware of this. This does not yield a numeric answer, simply the rate of change in terms of the other variables.
Oct
2
asked Help with this related rates problem.
Sep
24
awarded  Autobiographer
Sep
24
accepted Why is this derivative not undefined at a given point?
Sep
24
accepted Problem reconciling this proof with what I know about the Reals.
Sep
20
asked Why is this derivative not undefined at a given point?
Sep
18
accepted Why does implicit differentiation work on non-functions?
Sep
18
asked Why does implicit differentiation work on non-functions?
Aug
22
awarded  Inquisitive
Aug
21
accepted Computing the standard part of $(3-\sqrt{c+2})/(c-7)$ where the standard part of $c$ is $7$
Aug
21
comment Computing the standard part of $(3-\sqrt{c+2})/(c-7)$ where the standard part of $c$ is $7$
Yep. I'm a moron. Thanks guys.
Aug
21
asked Computing the standard part of $(3-\sqrt{c+2})/(c-7)$ where the standard part of $c$ is $7$