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 May15 comment TI Nspire CX CAS fails to perfrom basic integration yes, I do understand it. May15 comment TI Nspire CX CAS fails to perfrom basic integration exactly, the same thing happens in Wolfram Alpha (aka web-based Mathematica) May15 comment TI Nspire CX CAS fails to perfrom basic integration that's what I presume the problem is too. Is there any way to define $y \neq 0$ on the Nspire CX? Apr16 comment Proving corollary to Euler's formula by induction Ah, ok; perfect! Thanks for the clear explanation! Apr16 comment Proving corollary to Euler's formula by induction Ah, ok. So if the walk is not closed then I need to count each edge twice, right? But yes, once this information is clear I should be able to convince myself of that. Apr16 comment Prove that if graph $G$ is a 3-connected planar graph then its dual must be simple. Since a cycle must return to its starting vertex, a cycle beginning in $G_1$ must end in $G_1$ (it may or may not cross into $G_2$). In other words, the cycle must cross the bridges between $G_1$ and $G_2$ never or an even number of times. So that means such a cycle can only occupy two of the three available edges or none at all. Supposing the first case, if we removed the 2-occupied edges as you suggest, aren't we going to get a self-loop in the dual going across the remaining edge, which is not a simple graph? Apr7 comment Number of storms in a rainy season Yea, I didn't think the expectation looked quite right either Apr6 comment Planar complete tripartite graphs Let me rephrase that last part. We need not concern ourselves with a $K_5$ because a $K_5$ cannot exist in an $n$-partite graph for $n\leq 4$ by definition. It can exist in a 5-partite graph or above. Apr6 comment Planar complete tripartite graphs Because in the case of $r\geq 3$ and $s+t \geq 3$ there exists a $K_{3,3}$. We need not be concerned with a $K_5$ because by the definition of $n$-partedness a $K_5$ shouldn't exist, correct? Apr1 comment number of edges in the complement of a complete bipartite graph as a function of $n$, the toal number of verticies Ah yes, I wrote the answer assuming connectedness Mar31 comment number of edges in the complement of a complete bipartite graph as a function of $n$, the toal number of verticies Turns out that the question was not worded correctly, I'll answer the question below how the professor intended it to be interpreted, but for all intents and purposes, you deserve the credit for helping me arrive at the conclusion and attempting to answer what was essentially a poorly worded question. Mar31 comment number of edges in the complement of a complete bipartite graph as a function of $n$, the toal number of verticies Ah, I just caught that now after reading my question again. Typo, my apologies. $n$ is the number of vertices, not edges Mar31 comment number of edges in the complement of a complete bipartite graph as a function of $n$, the toal number of verticies correct, I understand that, but $n$ is the total number of vertices, which is still $p+q$ Mar31 comment number of edges in the complement of a complete bipartite graph as a function of $n$, the toal number of verticies how can $pq=n$? isn't $n= p+q$? Mar31 comment Expectation of a Poisson Process Right up top, unless I'm missing something, first one. Can't miss it. They use X and Y there rather than W Mar30 comment Prove for a simple graph that $n-1 \leq m \leq \frac{n(n-1)}{2}$ exactly, that's what I'm not sure about. I can show that the other extreme is true as well by removing any $3$ edges. Removing any more than that makes the graph disconnected and the inequality would fail. However, I'm not exactly sure that showing this for the extreme cases would be considered a "proof" Mar30 comment Prove for a simple graph that $n-1 \leq m \leq \frac{n(n-1)}{2}$ 0oo, I didn't know I could use MathJax in titles too. thanks for the fix and teaching me something new Mar30 comment Expectation of a Poisson Process I did, I'm not quite understanding. as far as I can tell from wikipedia, the inner function would be a function of $x$ en.wikipedia.org/wiki/Law_of_total_expectation Mar30 comment Expectation of a Poisson Process @Did Maybe it's a notation thing, this subject has a lot of different notations, but the inner expectation should be a function of $x$ and the outer one should turn it into a number, correct? Mar27 comment Expectation of a parallel system What is $H_n$, the heavyside step function?