Daniel came over to HQ yesterday to visit me, though i think playing pool was his most imporant objective. Anyway, glad to know that i Can still beat him in pool, or maybe it was just him pitying a sick patient, but i doubt so XD. (Anyway i wasn't playing seriously daniel!) Goes to show that the cue really doesn't make much difference in gameplay. At least thats what i think. Besides, I feel that I am living proof that n the hands of a capable pool player, all shots that can be done with a thousand-over-dollar 314 predator cue can also be done with a cheap 10 dollar 2nd-hand cash converters cue, albeit with as much effort. Thus i despise people with expensive cues XD. In fact a normal new cue worth about 100-200 dollars is about as good enough a cue as you'll ever need unless you're a professional pool player. And no, i don't think anyone in Singapore qualifies to be proffesional. My idea of a professional pool player is a person who can survive solely on playing pool. And that excludes coaching, setting up pool parlours.. etc...
Okay, enough of all the pool and hot air. Lets move onto the real fun and the real world. Mathematics. Indeed, Mathematics is the code that the world is designed with. Equations and laws in physics, chemistry, engineering that so accurately describes the real world are written and explained not philosophically nor spiritually, but mathematically.
If there was indeed a God, he would have hidden mathematical secrets into the laws of the real world. By studying and revealing these laws, we are discovering the creator's little treats. And that makes Euclid's Elements more religious than the holy bible!
Jokes aside, lets get onto some serious fun.
Today, we will show that the harmonic series diverges. Known since about the 1300's. If you can't follow this proof, either i am a very bad explainer or that your level of intelligence is 700 years old!
The harmonic series is 1+1/2+1/3+1/4+1/5+1/6.... and so on. Upon looking at this series, most people's reaction would be that the series converges to a value, since the terms ultimately becomes zero. Indeed, the fact the the individual terms become zero is a neccesary but not sufficient condition of the convergence of a series. If the terms do not zoom off to zero fast enough, it is still possible that the entire value of the sum diveges(becomes infintiy).
To the actual calculations.
S=1+1/2+1/3+1/4+1/5+1/6..
notice that we can group the terms like this.
S=[1]+[1/2]+[1/3+1/4]+[1/5+1/6+1/7+1/8]+.....
S=1+1/2+1/3+1/4+1/5+1/6..
notice that we can group the terms like this.
S=[1]+[1/2]+[1/3+1/4]+[1/5+1/6+1/7+1/8]+.....
Each of the grouped terms is more than 1/2.
Since there are an infinity of grouped terms, there an infinite number of terms more than half, and thus S is infinity as well..
But the divergence is extremely slow.. Indeed no computer would even hint at its divergence in a short period of time. For example. if we sum up the first 10^43 terms we would only get something less than 100.
But the divergence is extremely slow.. Indeed no computer would even hint at its divergence in a short period of time. For example. if we sum up the first 10^43 terms we would only get something less than 100.
Which is like. tiao-.-
Just goes to show that mathematicians are smarter than computers:D.
(more hot air)
In the next post i'll show why people who can go to jc but choose to go poly are (in my opinion) idiots-Mathematically..
1 comment:
that was stupid and a huge waste of time. never do that again!
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