Recent content by Gavran

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    Undergrad Non-Linear Infinite Resistor Ladder

    The limit is irrational, and the primary objective now is to provide a rigorous proof of its irrationality.
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    Undergrad Prove that 1 + NOT (1 + NOT x) = x

    We can define the function ## f(x)=1+\text{NOT}x ## and prove that ## f^{-1}(x)=f(x) ##. ## \begin{align} f(x)=1+\text{NOT}x&\implies f(x)-1=\text{NOT}x\nonumber\\ &\implies \text{NOT}(f(x)-1)=x\nonumber\\ &\implies f^{-1}(x)=\text{NOT}(x-1)\nonumber\\ \end{align} ## For $$...
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    Undergrad Non-Linear Infinite Resistor Ladder

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    Physics Jokes!

    A little boy refused to run anymore. When his mother asked him why, he replied, "I heard that the faster you go, the shorter you become."
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    Undergrad Comparing the time of two moving clocks

    Mermin, N. David. Space and Time in Special Relativity Chapter 10 (pages 87-90) “Why He Says My Clocks Go Slowly Although I Know that His Go Slowly” https://dokumen.pub/qdownload/space-and-time-in-special-relativity-1stnbsped.html
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    Undergrad Proof of Asymptotic Equality: $\sum_{n=0}^\infty a_n\frac{x^n}{n!} \sim ae^x$

    It seems to me that you did not show that ## \sum_{n\ge0}(a_n-a)\frac{x^n}{n!}\sim0 ##, which is crucial to the proof.
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    Art Some more of my photography

    My three favorites:
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    Dividing a $100 bet three ways to guarantee equal payoff

    I would rather use “Suppose there are ## n ## possibilities and those (precisely) ## n-1 ## must happen.” Therefore, if the USA wins, two events happen: the first one is “Great Britain does not win” and the second one is “China does not win”. The event “the USA does not win” does not happen...
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    Art Please rate my photos on a scale of 1-5

    5/5 5/5 3/5 3/5 1/5 5/5,5/5 5/5 2/5 5/5
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    Hedging on a weather prediction

    Your results are correct. The expected value of a profit (or a loss) in the case of a fair bet must be equal to zero. ## E(\text{Profit}_{Ra})=3\cdot P_{Ra}(sun)-2\cdot P_{Ra}(rain) ## ## E(\text{Profit}_{Ra})=3\cdot 2/5-2\cdot 3/5 ## ## E(\text{Profit}_{Ra})=0 ## ##...
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    Undergrad The problem of points

    The third method from the original post is criticized mostly for the case in which player A has one winning round and player B has a zero winning round when the interrupting event occurs. Applying the third method in this case, the whole prize pot is awarded to player A, although he has only one...
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    Undergrad The problem of points

    There are many versions of this problem with different scores and different interrupting events. One interesting scenario is a scenario when the game is interrupted by police because the game is organized illegally. The original problem statement is “A company [two players] plays a ball game to...
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    Undergrad Why ##a^0=1##?

    @symbolipoint, thank you. In any of the earlier posts, nobody mentioned the solution for ## 0^0 ##. Using post #8 for defining ## 0^0 ## will generate the result ## 0^0 =0^{x-x}=0^x/0^x=0/0 ##, which is undefined. The mathematical expression ## 0^0 ## has different interpretations, and it is...
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    Undergrad The problem of points

    Two players, A and B, are playing a game, and the probability that either player wins a round is 1/2. They contribute equally to a prize pot. The game ends when one of the players wins six rounds. The game is interrupted for some reason when player A wins 5 rounds and player B wins 3 rounds. How...
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    High School Multiplication and Division by Numerical "Trituration"

    Can you provide any reference where these methods are called "multiplication and division by numerical trituration"?
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