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    More primes

    I saw this on a website. Prove that if r and s are positive integers with r > s and gcd(r,s)=1, then gcd(rs , r + s)= 1. I can think of two ways to show this. Using the Euclidean algorithm or by showing that 1 can be a linear combination of rs and r + s. Funny thing...I couldn't do either...
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    Graph theory (connectedness)

    I remember when I was taking discrete analysis of data structures and we had to prove certain graph theory properties. I'll give a specific example, prove that the cycle graph, C_n, is connected for all n. From what I remember, it was induction we used to prove this...what I want to know...
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    Wireless Antenna Strength

    Ok. I'm currently trying to understand antenna strength in the wireless cards you find for your computer. Let's say that I have a wireless http://www.tigerdirect.ca/applications/SearchTools/item-details.asp?EdpNo=706706&Sku=D700-2286" with a certain "receiver sensitivity". How exactly do I read...
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    Continuous function sends closed sets on closed sets

    Let f: D \rightarrow \mathbb{R} be continuous. Is there an easier function that counterexamples; if D is closed, then f(D) is closed than D={2n pi + 1/n: n in N}, f(x)=sin(x) ????? Plus, these counterexamples are very similar ...but are they correct? If D is not closed, then f(D)...
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    Continuous functions

    Let f: D \rightarrow \mathbb{R} be continuous. Is there an easier function that counterexamples; if D is closed, then f(D) is closed than D={2n pi + 1/n: n in N}, f(x)=sin(x) ????? Plus, these counterexamples are all the same with the domain changed, just correct me if I'm wrong...
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    Running in the rain

    I recently saw an episode of mythbusters where they tested the theory that if you run in the rain you get less wet. Their results turned out to be the exact opposite, they found that running in the rain actually made you more wetter. I'm wondering now, taking into account only the "falling" rain...
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    Boundary question

    Is it possible for a set's boundaries to contain some interior points? I can't think of an example off-hand...one would be nice.
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    Check my logic

    Ok..tried to help a friend understand some of his homework..I haven't seen symbolic logic since college, but there was this one problem in particular that went something like..."Mr. X got a C on his final." and "Mr. X passed the class"...we say that these are represented by p and q...
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    Check my logic

    Ok..tried to help a friend understand some of his homework..I haven't seen symbolic logic since college, but there was this one problem in particular that went something like..."Mr. X got a C on his final." and "Mr. X passed the class"...we say that these are represented by p and q...
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    Lightning bolt power and Back to the Future

    This is the second time I write this post because the first time it got deleted...so I must say that I am not going to go into all the detail that I went into the first time I wrote this..not to mention that I'm a bit p.o.'d. In back to the future, doc brown says that a lightning bolt can...
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