hardmath
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 51m revised $\lim_{x \to 4} \sqrt{x^2-16}$ gave three instances of defining limit from elementary calculus and pre-calculus texts 4h comment $\lim_{x \to 4} \sqrt{x^2-16}$ I'll include a definition from a typical calculus or pre-calculus text by editing my answer. 4h comment $\lim_{x \to 4} \sqrt{x^2-16}$ If your teacher has prepared the class notes and you cannot find a definition of limit there, it is reasonable to ask. 5h comment Number of elements in $S^{-1}(\mathbb Z/6\mathbb Z)$ Sorry, it was me from the reopen review queue, and I misinterpreted the big set of things you started with. 5h revised Number of elements in $S^{-1}(\mathbb Z/6\mathbb Z)$ minor edit to fix misconceived downvote 5h comment Number of elements in $S^{-1}(\mathbb Z/6\mathbb Z)$ @Stahl: My mistake, you are correct that the images of $S$ are units. I misstated how they may get mapped to the same unit, in this case $1,3,5$ all "go to the same unit". 5h comment $\lim_{x \to 4} \sqrt{x^2-16}$ Okay, but there should be a definition of limit given in the notes. Is this a calculus or a pre-calculus class? 6h comment A union of n sets with diferent order, how can I prove? Nothing personal, Samuel. To you the connection between what you "hinted" and the proof asked for in the Question is probably clear. However it will not serve as an Answer without more than the one line you wrote. 6h comment Frog leap game - error anaylsis For the first part, estimating the individual "transition" probabilities, you may benefit from the Wikipedia article Binomial proportion confidence interval‌​. Depending on the choice of distribution for $p_i$ errors of approximation, the second part amounts to propagating the uncertainty of the $p_i$ factors into their total product. 6h reviewed Leave Open Why are these different ? $y^2=2x^2+C$ vs. $y=\sqrt{2x^2}+C$ 6h reviewed Close Intuition behind the Jacobi triple product 6h reviewed Looks OK Would such a function be of any importance (primality test)? 6h reviewed Delete A union of n sets with diferent order, how can I prove? 6h comment A union of n sets with diferent order, how can I prove? This is a true statement, and perhaps it could even be used in a proof of the statement about rearranging the order of sets in a union. But absent more of those details it hardly answers the Question. Perhaps you should consider whether this even rises to the level of a constructive Comment. 6h reviewed Reopen Prove an identity in a Combinatorics method 6h reviewed Reopen Number of elements in $S^{-1}(\mathbb Z/6\mathbb Z)$ 6h comment Are you sure the following is true or not.:$(0.\overline{9}=1 )$ Are you asking whether $0.9999\overline{9}=1$? The slash usually indicates division, but I have a hard time believing you want to know if zero divided by something (nine?) is equal to one. 8h comment What are some measures of connectedness in graphs? @user929304: One concise book I'm fond of is Alan Gibbon's Algorithmic Graph Theory, and my copy is a well-thumbed paperback. A free (open source) book of the same name (different authors) is here, at Google Code. Note in particular Chapter 5, Distance and Connectivity. Community detection is a cottage industry unto itself because of interest in "data-mining". Probably the best approach is to find problems that interest you and ask for references specific to those. 10h comment $\lim_{x \to 4} \sqrt{x^2-16}$ To make it clear, let's look at the definition in your textbook. What is the title and author? 12h comment Frog leap game - error anaylsis You describe setting "the frog at vertex $i$ for $n_i$ times" and counting how many times it proceeds to jump to vertex $i+1$. This suggests that while the graph is "complex" you have some knowledge of it. In particular, do you know how many alternative possibilities for the frog's jump there are from vertex $i$? In graph theory terms, the out-degree of vertex $i$?