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 Necromancer
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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.
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.
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
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.
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.
Apr
15
comment Help verifying my proof that for any $\epsilon>0$, there exists rational $\frac{j}{k}$ such that $0<\frac{j}{k}<\epsilon$
I didn't know about the Archimedean Property... Thanks for pointing that out.
Apr
15
comment Help verifying my proof that for any $\epsilon>0$, there exists rational $\frac{j}{k}$ such that $0<\frac{j}{k}<\epsilon$
Clarity seems to escape me. I don't know why I didn't think of that.
Mar
27
comment Proving that if $\frac{m}{n}<\sqrt{2}$ then there exists $\frac{m'}{n'}$ such that $\frac{m}{n}< \frac{m'}{n'}<\sqrt{2}$
I like this, but at this point in the book, Spivak hasn't covered limits...
Mar
25
comment Proving that $\sqrt{2}+\sqrt{3}$ is irrational
This is clever and very simple. I barely missed this idea. I was trying to do stuff with conjugates, but didn't quite connect the dots.
Mar
25
comment Proving that $\sqrt{2}+\sqrt{3}$ is irrational
Oddly, those didn't come up when I searched. I saw those after posting and was going to close, but then people started answering. Still, it's been helpful.
Mar
18
comment Proof that $\binom{ n}{k} \in \mathbb N$
That's probably my biggest complaint about the text. For the most part, the exercises are very illuminating. Every once in a while though, I get a problem like this that really makes me wonder what he's trying to show here.
Mar
18
comment Proof that $\binom{ n}{k} \in \mathbb N$
Most of the proof exercises in Spivak seem to follow directly from the text. I had to incorporate quite a bit of outside knowledge to do this one, which makes me feel like I'm missing the point...
Mar
16
comment Help with this inequality.
Nvm, I figured it out.
Mar
16
comment Help with this inequality.
I caught the triangle inequality, and I'm clear on the cross multiplication... I just don't know what's happening between steps two and three. To be more specific, where is $0<\frac{|y_0|}{2}<|y|$ coming from? Sorry, I'm a little slow.