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Riemann Zeta Function

Imagine a sum that keeps getting bigger: 1 + 2 + 3 + 4 + ... but somehow, its "value" is said to be  \[1+2+3+4+5… = -\frac{1}{12}\] This equation isn’t a joke. It isn’t a typo. And it definitely isn’t like one of those internet tricks that try to prove that 2 = 3. But how? Doesn’t calculus dictate that the sum should diverge? How can an infinite sum of positive integers result in a negative fraction? This equation is one of the paradoxical results of the famed Riemann Zeta function: \[\zeta(s) = \sum_{n=1}^{\infty} \frac{1}{n^s}\] First Encounters My first encounter of the Riemann Zeta function was in a problem introduced to me in Math circle India:\(\newline\)               What is the probability that two random numbers x & y are coprime i.e. gcd(x,y) = 1 for \(  x,y \in \mathbb N\) At first glance, it seems like an impossible question to compute. We’re picking 2 numbers at random — how do you even define a probability over an...

Casinos: Bright light attractions or daylight robbers?

Ah! Casinos! The lights! The thrills! The lotteries!!, but wait, it has a dark side. Many of you adult readers may or may not have gone to a casino, but did you know that it is the biggest theft industry that is approved by the government? That's right, the casinos have a carefully calculated system that wins most of the time without being too suspicious and you can't even beat smart with smart as it is against the law to use any shred of intelligence there. How do casinos do this? Let's find out.

Casinos use the mathematics of probability, in simple probability, the probability of a coin landing on heads is equal to it landing on tails because of there being two sides. Even with more sides, the probability is always 100%/ number of sides. But how can such giants make is much money with such a small concept? They don't. That was just a simple representation of probability but casino's take in account every small detail, the spin, the momentum, the velocity, everything! Using all that data they create a system which allows them to cheat while keeping the general public playing.

So Casinos are big theft industries, so how are they compatible with the law? The government allows the casinos because they are good for the economy. How? Easy, the big casinos attract so many tourists every year, it practically keeps the economy afloat. So, it is my request to you, no matter how lucky you feel, don't go straight to the thieves den. If many people do this, sure, the economy will go down a bit, but in the long run, it will rid us of those theives that rob us right under the police's nose.

Comments

  1. Nicely written Aarit. As they say - "House always win!". Now we know why.

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  2. Interesting theory but as long as one remembers that gambling is entertainment and not a sport, it is possible to enjoy a casino wiyhiur going bankrupt!

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  3. Well presented. True Aarit.
    ( Fact is :- Hardly few persons come out by winning little. Majority go spend , loose & come. Still craze for going to Casino hasn't reduced ๐Ÿ˜Š, though they are aware of the set-up. For e.g I lost Rs1.25 lacs in Singapore Casino but still I went there next day to try my luck & enjoy )



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  4. Wow, so well put. Great workk๐Ÿ’ฏ

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  5. Very true Arit. But u r too young to understand it so how come you know so much

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    Replies
    1. I have read all of this from a book called Alex's adventure in Numberland

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  6. Brilliantly articulated Aru, looking forward to read more interesting articles!!

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