My last class session was basically my "teacher" telling us that some infinite sets are countable and others are not.

Hello? The set is infinite. How do you count an infinite number of items? The cardinality of a set of infinite items is infinity.

Teacher: "The cardinality of an infinitely countable set is 'aleph null'."

Bitch! INFINITY = ALEPH NULL. You are wasting my precious time with your application-less math!

Help.

-Warik

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Oh well, at least this way I might get a fellow C.S. major to comment. A few of my friends who already have a computer programming job all replied in the same way when I asked if Discrete Math was of any use in the programming world: "lol" followed by "that class is bullshit."

-Warik

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1) The kind who are too dumb to finish.
2) The kind who are too smart and end up getting jobs before finishing.

Two of my friends were #2 (one of them didn't even finish a semester, lol). If I have to take more BS classes like this, I'll probably join #2.

-Warik

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I don't know which pisses me off more, the fact that my book says that the set of positive integers is countable or the fact that my book says that the set of real numbers is NOT countable even though the positive integers are.

I think the only real-world application for discrete mathematics is being a discrete mathematics professor.

-Warik

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The fact that a college degree is wanted for most jobs is absolutely ludicrous. I vow, with the entire Elite Fitness population as my witnesses, that if I choose to start my own software company, a college education will *NOT* be a factor in the hiring of an employee. Hell, I'd rather hire a young guy who learned everything that he knows from books, Internet sites, and sample code than hire a guy who wasted 3-4 years of his life being taught by other people things that he couldn't learn on his own.

Give me $1,000 to spend on a shopping spree at Barnes & Noble and my college education won't mean a damn thing.

-Warik

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As for the discrete math - I haven't ever had to use it in my programming and most people wouldn't. In my opinion if you want to go ahead and teach CS or if you want to really know why things are the way they are, then you need to know all the lowest level stuff and really know the math behind it.

but in everyday life you aren't proving that this is working b/c of this, you are just using it - and most things you are using are well known functions anyway (everyone knows which search algs to use and such).

I always enjoyed math, but if you aren't liking it, then I feel your pain - I always hated Latin and French - I have a learning disability or something when it comes to languages - I can learn any programming language in like a day or two, and math and science, no prob - but languages I'm at like a retarded 3rd grade level.

I feel like JohnnyO has set me up for some kind of display of monster wisdom - which I am unable to provide.

I'm afraid there isn't a reasonable answer to your question. Discrete mathematics will come back into your life if you are a math professor. That's about it. The same can be said of Number Theory - I put considerable effort into that also. I had a maniacally passionate professor for Number Theory - a very intelligent man - expending huge sums of calories attempting to teach us this almost worthless concept.

At least Number Theory can help in solving some systems of equations.

If it makes you feel any better, I had to take two CS classes to get my math degree, and at that time I had no desire to be a tech guy, so I took Fortran and intro to C++, and got nothing out of it.

The only thing that comforts me is the knowledge that it's a bullshit class. I don't need to learn the material. It's not like my advanced C++ class where if I don't understand a concept, then I'll get screwed later in life.

I'm willing to settle for a B in the class. The problem, however, is that I might actually have to pick up the book and read it. =(

-Warik

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The reason that the set of real numbers is not countable is the this:

{1,2,3,4,5...,and so on} in this set of integers there is no number in between. In other words from 1 to 2 there is no other number, hence it is a countable set {1,2,3,4,5} is countable.

{1.0,2.0,3.0,... and so on} in this set the of real numbers there is are infinite sub-sets of real numbers hence it is an uncountable set.

{1.0,2.0,3.0} while this seemingly innocent looking set of numbers seems countable we cannot count all the possible number combinations in between just two of the numbers say 1.0 and 2.0

For example divide the space into half therefore 1.0 to 1.5, divide this again in half, 1.0 to 1.25 and so on. As you can see you will never get to 1.0 nor could you ever get to 2.0 by increasing it.

It is easy to see why the set of real numbers is uncountable.

In programming for engineering and physics one must be expressely aware of this because it could cause problems in a mathematical model of some physical reality being modeled (or theoretical reality) Quantum mechanics, finite element modeling computational fluid dynamics solving statistical problems and partial differential equations.

While you will more likely be an applied cs person just as I have my minor's in applied mathematics we for the most part will not need to know the particulars of pure math, but it is good to have an firm understanding on the basics of it.

Hope this helps and I wonder how much of it I remembered correctly.

Go Matt.

My book defines an "infinitly countable" set of numbers as a set of numbers whose elements can be listed in a sequence whose index is the set of natural numbers. Like, if you take an element n from the set N and enter it into the equation y = 2n - 1, y will always equal an odd positive integer, and for y = 2n, y will always equal an even positive integer. That brings me to the next question, who arbitrarily decided that we will base infinite countability on the set of natural numbers. Hell, the set of natural numbers is not countable! How many elements are in the set of natural numbers? I can't think of a single answer besides "an infinite amount" or "aleph null" which I am convinced is just a synonym for infinity.

I don't know if any of this will help me in my future entertainment software (games!) development career, but I suppose I will find out in time. For now, I'm stuck taking the class unless I do what my friend did. He took all of the classes that he felt were important, didn't take the rest, and just went out and got himself a job. lol...

Thanks again, everyone.

-Warik

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i LOVED number theory, and had a great professor for that class, but discrete was taught by a senile visiting professor from arkansas. i don't remember anything from the class (though you're dredging up some bad memories with this discussion) other than my moronic professor spending some time on something called the "pigeonhole principle", which states:

If m pigeons are put into m pigeonholes, there is an empty hole iff there's a hole with more than one pigeon.

Thanks. I learned something today.

I hear you on the Real vs Integer thing.....Real Numbers include the Irrational Numbers...etc...

Our current way of counting could have involved many different schemes. Whether we use base 10 or base 6 doesn't matter. The fundamental rules of mathamatics is a constant in the Universe. Look at it this way, is zero a number? or is there a number in the infinite group or beyond?

take the limit of x as it goes to zero either from the negative or positive side in the equation 1/x. The answer is infinity. But if you divided by zero explicitly the answer is undefined.

Now take the limit of x as it approaches infinity for the same equation, the answer is zero. In fact no matter the number in the infinite set or beyond the answer will always be zero.

But back to counting and math. We most likely ended up using or adopting the base 10 system because we have ten fingers. It may seem strange but if you think about it we learn to count using our fingers so it would be natural to develop our system based on the number 10.

My books are packed and my memory is weak. Hope this helps you a little more.

quote:

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Originally posted by mrbill:
Warik...it doesn't matter what field your in, you will always have to take a certain number of "bullshit" classes. It's just part of the college experience...plus its a way for them to suck more money out of you.

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Lol, if it's only money that they're after, I'd gladly pay them anyway. It's not my money anyway. It's scholarship money funded by the Florida lottery (aka, the "stupid tax").

-Warik

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