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Please note that I have another blog at translateparadox.blogspot.com.

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Want A Pet?

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Want a Pet?           Would you like to own a pet? I would want a pet dog or cat because they remind me of good friends. However, they would need to meet certain requirements, such as being hypoallergenic and friendly. I would love this kind of pet.           I used to have a best friend named Joshua about 5 years ago. We lived directly across from each other and played a lot together. We played new games and old every day from right after school to when we had to sleep, and we often ate together. We even sometimes went together to fun places like amusement parks and water parks. He had 4 cats that were really nice, but I was allergic to them. My mom had to give me allergy medicine every time I went over to his house. When I had a mild allergic reaction to them, it was very annoying, especially if I was playing. I would like to have a cat like Joshua’s except it will have to be hypoaller...
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March 25, 2015 A Google a Day

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Sorry again for not doing yesterday's A Google a Day. Well, here is today's! Question #1 Category: Pop Culture Question: What was the profession of the man who served as foster father to the title character of a 1980's sitcom about a little girl and her dog, Brandon? Total Points: 300 points Hint: George First Letters: P _ _ _ _ _ _ _ _ _ _ _ Answer: Photographer  (I wonder if he got the idea from OneNote) Question #2 Category: Sports Question: In Jeff Savage's book on the 2005 number one pick for the NHL draft, what is the title of the second chapter beginning on page 10? Total Points: 600 points Hint: Penguin ("whaddya think, Penguin?") First Letters: S _ _ T _ _ K _ _ Answer: Sid The Kid (obviously, Jeff is a *little* childish) Question #3 Category: Art Literature Question: In "Eats, Shoots and Leaves", what analogy does the author say that grammarians use for the relationship of punctuation to words? Total Points:...
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Original Math Proof - When does y=b^x intersect the line y=x if b>1?

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When does y=b^x intersect the line y=x if b>1? by Joseph Kim at josephkimlife.blogspot.com February 2019 \text{If } y=b^x \text{ and } y=x \text{, then }x=b^x \text{ and }b = x^{1/x} \text{. We would like this to have only one} \text{solution for } b>1 \text{. Now we will prove that }b \leq e^{1/e} \text{ :} \begin{align*} \lim_{n\rightarrow \infty}{\left(1+\frac{1}{n}\right)}^n &= e \\ \lim_{m\rightarrow 0}{\left(1+m\right)}^{1/m} &= e \\ (1+m)^{1/m} &\leq e \\ \text{(with equality only } &\text{when m=0)} \\ 1+m &\leq e^m \\ 1+\frac{(x-e)}{e} &\leq e^{(x-e)/e} \\ \frac{x}{e} &\leq e^{x/e-1} \\ x &\leq e^{x/e} \\ x^{1/x} &\leq e^{1/e} \\ b &\leq e^{1/e} \\ \end{align*} \text{Note that, in the above proof, we must have } b\geq0 \text{, but we are already restricted to } b>1, $\text{so this condition is irrelevant. Under this restriction, } e^{1/e} \text{ is an absolut...
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