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Striker

Striker

Member Since 10 May 2009
Online Last Active 4 minutes ago
***--

So, I heard you like trucks?

Today, 01:39 AM

 

Who wants to race?


Welcome to the YCM Dungeon

14 November 2017 - 03:59 AM

A little taste of what goes on in the YCM Dungeon, brought to you by the Angry Video Game Nerd himself. I hope you never have to experience this place for yourself.
 


E.T. the Extra-Terrestrial (Atari 2600)

09 November 2017 - 12:23 AM

Etvideogamecover.jpg

https://en.wikipedia...al_(video_game)

 

Considered to be one of, if not the worst video game in history, ET is often cited as the game that lead to the 1983 North American Gaming Collapse, and it is considered a lesson in what can happen when a game is severely rushed (ET was done in only five weeks). It underwhelmed sales predictions so much that the remaining stock was buried in New Mexico in late 1983 and then discovered in 2013. I personally haven't played the game, but it's on my to do list with all these retrogames on my laptop. Anyway...

 

To get a discussion started, do you think ET deserves to be called the worst video game in history? Do you think it is the main reason it lead to the 1983 collapse? Why or why not?

 

Note for Mods: If this isn't an adequate thread for this section, feel free to move it and let me know so I can learn for the future.


Strange/Interesting Mathematical Phenomena

03 November 2017 - 02:53 AM

What are your favorite mathematical concepts that are strange due to them violating preconceived notions or are just interesting? To get this topic started, let me show you a proof of one of my favorites: the probability of hitting a rational number in the set [0,1] is zero.

 

Before we begin, let us define the Lebesgue Measure. In essence, it is a way to measure subsets of Rn (for a more detailed definition, click on the above link). For our purposes, we are interested in the following property: the Lebesgue Measure of a closed interval [a,b] is m([a,b]) = b-a, where a < b. Using this property, we can find the Lebesgue Measure of both the interval [0,1] and Q, where Q denotes the rationals.

 

The Lebesgue Measure of [0,1] is trivial to find as it is a direct application of the property in question: m([0,1]) = 1.

 

The Lebesgue Measure of Q is not as straight-forward to find. In order to motivate this result, let us consider the following: Q = U(qi). What this says is that Q can be thought up as the union of an infinite number of rational numbers qi (there are a countably infinite number of rational numbers). This separation of Q allows us to use our property above: m(Q) = m(U(qi)) = sum(m(qi)) = sum(0) = 0, where sum() is the summation function.

 

So, we have that m([0,1]) = 1 and m(Q) = 0. This is enough to show that the probability of hitting a rational number in the set [0,1] is zero, but it begs the question of what makes m([0,1]) = 1 if m(Q) = 0. Well, we can define the irrational numbers as R/Q, which denotes the set of elements of the real numbers that are not in the set of rational numbers. As we are concerned with the set [0,1] and not R, we can redefine the irrational numbers as [0,1]/Q. Now, the m([0,1]) = m(Q ∩ [0,1]/Q) = m([0,1]/Q) = 1. Therefore, the Lebesgue Measure of the irrationals in the set [0,1] is 1.

 

The above result not only suggests that the probability of hitting a rational number in the set [0,1] is 0, but it also suggests that the probability of hitting an irrational number in the set [0,1] is 1. Now this makes sense since P(S) = 1, and we have defined S to be S = [0,1] in our example.

 

And with that, let us discuss the topic at hand: What are your favorite mathematical concepts that are strange due to them violating preconceived notions or are just interesting?


Ask Striker Anything

05 October 2017 - 11:56 PM

I'm just about finished with Week 2 of 10 of Fall Quarter, and it hasn't been as time consuming as I thought it'd be; therefore, I might as well answer whatever silly, serious, or overall random questions y'all have in mind. So, don't hold back, hold nothing back tonight.