May
26
accepted proving that $-1$ and $1$ are the only units in $Z$, using the given axioms
May
26
revised proving that $-1$ and $1$ are the only units in $Z$, using the given axioms
added 48 characters in body
May
26
comment proving that $-1$ and $1$ are the only units in $Z$, using the given axioms
Oops, I left out the associativity axioms by mistake! I am intrigued by your comment that the well-ordering axiom might be enough to prove associativity. Are you sure that's true?
May
25
comment proving that $-1$ and $1$ are the only units in $Z$, using the given axioms
I did realise that $0 = 1$ meant there was only element but - as you said - that couldn't have been the intention. But I'm not sure if the 4th and 5th axioms imply $0 \neq 1$. In any case, even after assuming $0 \neq 1$. I should've realised - as you pointed out - that the same axioms are satisfied by $\mathbb{Q}$ and $\mathbb{R}$ so clearly something was missing. Although I like the book's approach (after the one day I spent with it), I'm not sure if missing the additional axiom was intended (maybe it's a feature of the inquiry-based approach?) or an oversight by the authors.
May
25
asked proving that $-1$ and $1$ are the only units in $Z$, using the given axioms
May
19
comment edge deletions and spanning subgraphs
you're right, I was reading more into the definition of $G-X$ than was there!
May
19
accepted edge deletions and spanning subgraphs
May
19
comment edge deletions and spanning subgraphs
@saulspatz that the subgraph induced by removing one or more edges from $G$ is necessarily a spanning subgraph of $G$, which the text appears to me to be implying.
May
18
asked edge deletions and spanning subgraphs
May
6
awarded Tumbleweed
Apr
29
revised should I be using `UIDocument` and/or `UIDocumentBrowserViewController` in my app?
edited tags
Apr
29
asked should I be using `UIDocument` and/or `UIDocumentBrowserViewController` in my app?
2017
Dec
8
answered Division of Factorials
Aug
6
comment strange choice of constant when showing $an + b = O(n^2)$ ("Introduction to Algorithms" book)
@miracle173 I guess your question stems from lack of context (as I only quoted the text relevant to my question). Taken from the beginning, the sentence actually goes: "What may be more surprising is that when a > 0, any linear function an+b is O(n^2)", the potential "surprise" according to the authors being an+b is not only O(n) but also O(n^2).
Aug
6
comment strange choice of constant when showing $an + b = O(n^2)$ ("Introduction to Algorithms" book)
@miracle173, I know an+b is O(n) (and even $\Theta(n)$). That was not the point of the question.
Aug
5
awarded Supporter
Aug
5
accepted strange choice of constant when showing $an + b = O(n^2)$ ("Introduction to Algorithms" book)
Aug
5
comment strange choice of constant when showing $an + b = O(n^2)$ ("Introduction to Algorithms" book)
Why do you feel I should remove it? I think it might help someone else making the same mistake as me. (btw if you were to post your comment as an answer I'd be happy to accept it.)
Aug
5
comment strange choice of constant when showing $an + b = O(n^2)$ ("Introduction to Algorithms" book)
@fade2black ah okay, I had missed the clause that $0 \le f(n)$. Thanks!
Aug
5
asked strange choice of constant when showing $an + b = O(n^2)$ ("Introduction to Algorithms" book)
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