What is the Axiom of Choice?
Truth be told, I'm a math geek and a genius. I have paperwork that tells me so, but I'll leave it up to you to form your own opinion. As for me, I'm just trying to get by in life and make the most out of every day, learn as much as I can, and push the people around me to be the best they can be (no this is not an Army ad).
The Axiom of Choice, as terrorist as it may appear, is really an important and fundamental axiom in set theory (it is also a band that I've never listened to). The axiom was formulated over a century ago by Ernst Friedrich Ferdinand Zermelo. It is considered by many math geeks and academics to be the last great controversy of mathematics. Enough of that...I got to Axiom of Choice via something that a college professor of mine used to love, Zorn's Lemma. Zorn's Lemma is stated as "If S is any nonempty partially ordered set in which every chain has an upper bound, then S has a maximal element. This statement is equivalent to the axiom of choice." To put it in terms that most people will understand, there is always a top element in any set of things. It has taken me years of reflective thought and wasted brain cells to understand my professor's fascination with this lemma. If you take it out of context of math terms, it means that if you have any group of people there are always people you can choose from, which means you always have a choice as long as there are options to choose from. This by no means matches what the mathematicians of the world will explain this as, but it works for me.
If you want to learn more about this fascinating topic, MathWorld is the place for you: http://mathworld.wolfram.com/ZornsLemma.html. You can also take a look at WikiPedia http://en.wikipedia.org/wiki/Axiom_of_choice. I think that I'm supposed to put this here as well: "Eric W. Weisstein. "Zorn's Lemma." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/ZornsLemma.html "
As for me, math theory is a lot like the opera. There are talented individuals performing great acts, all of which I can appreciate, but none that truly touch my soul. I will always be able to appreciate it for the art that it is, but never truly understand it.
For me, mathematics was always a way to count things, put things in order, and look for relationships between them. I noticed at an early age that the difference between two squares always equaled the sum of the first number plus the number after it. For those of you having trouble keeping up, (5*5)-(4*4)=9 which is 5+4. So if you know 1 squared, you can find the rest of them. Keep in mind, I was 9 when I figured this out....So I didn't know anything about algebra. I later learned that this is simply (X+1)^2-X^2. Which once you work it out is (X+1)+X. Which a guy named Fibonacci proved a long long time ago. For me, I think it was some sort of autistic pattern recognition.
Why all the math talk you're probably wondering? For me, it helps to put things in perspective. You see, I spend my days and my time trying to break computers at all levels. I am constantly looking for new ways to combine parts to produce an error that nobody looked for before me. It is this freakish gift of looking at a vast amount of variables and seeing a minimal path through for maximum return that gets me through most days.
My days you ask, how do I spend them? Well I manage a test team responsible for testing products like our customers will use them. This has always been something that I've done. It gives me a chance to not really have to ever build something, but to sit back and find fault in it. (I come by it naturally, lack of positive feedback as a child.) It is the career path that chose me, so I've stuck with it. I get the opportunity to make things better, build relationships with people that I get to tell on a daily basis they did their job wrong, and I get paid for it. I've been fortunate to actually see some of the things I've worked on in my life get sold for profit, and I've seen some shelved for reasons that only the deity of your choice knows why. It is satisfying for me to see my product and efforts be successful and allow other people to make a difference, learn something new, or make a living from it.
This about does it for my first blog post. If you've gottent this far, thank you for reading my whole post. Please stay tuned for more rambling thoughts from a depressive nymphomaniacal insomniac. And remember, you always have a choice. You may not like all of the options, but you always have a choice.
Affectionately yours. Gio
The Axiom of Choice, as terrorist as it may appear, is really an important and fundamental axiom in set theory (it is also a band that I've never listened to). The axiom was formulated over a century ago by Ernst Friedrich Ferdinand Zermelo. It is considered by many math geeks and academics to be the last great controversy of mathematics. Enough of that...I got to Axiom of Choice via something that a college professor of mine used to love, Zorn's Lemma. Zorn's Lemma is stated as "If S is any nonempty partially ordered set in which every chain has an upper bound, then S has a maximal element. This statement is equivalent to the axiom of choice." To put it in terms that most people will understand, there is always a top element in any set of things. It has taken me years of reflective thought and wasted brain cells to understand my professor's fascination with this lemma. If you take it out of context of math terms, it means that if you have any group of people there are always people you can choose from, which means you always have a choice as long as there are options to choose from. This by no means matches what the mathematicians of the world will explain this as, but it works for me.
If you want to learn more about this fascinating topic, MathWorld is the place for you: http://mathworld.wolfram.com/ZornsLemma.html. You can also take a look at WikiPedia http://en.wikipedia.org/wiki/Axiom_of_choice. I think that I'm supposed to put this here as well: "Eric W. Weisstein. "Zorn's Lemma." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/ZornsLemma.html "
As for me, math theory is a lot like the opera. There are talented individuals performing great acts, all of which I can appreciate, but none that truly touch my soul. I will always be able to appreciate it for the art that it is, but never truly understand it.
For me, mathematics was always a way to count things, put things in order, and look for relationships between them. I noticed at an early age that the difference between two squares always equaled the sum of the first number plus the number after it. For those of you having trouble keeping up, (5*5)-(4*4)=9 which is 5+4. So if you know 1 squared, you can find the rest of them. Keep in mind, I was 9 when I figured this out....So I didn't know anything about algebra. I later learned that this is simply (X+1)^2-X^2. Which once you work it out is (X+1)+X. Which a guy named Fibonacci proved a long long time ago. For me, I think it was some sort of autistic pattern recognition.
Why all the math talk you're probably wondering? For me, it helps to put things in perspective. You see, I spend my days and my time trying to break computers at all levels. I am constantly looking for new ways to combine parts to produce an error that nobody looked for before me. It is this freakish gift of looking at a vast amount of variables and seeing a minimal path through for maximum return that gets me through most days.
My days you ask, how do I spend them? Well I manage a test team responsible for testing products like our customers will use them. This has always been something that I've done. It gives me a chance to not really have to ever build something, but to sit back and find fault in it. (I come by it naturally, lack of positive feedback as a child.) It is the career path that chose me, so I've stuck with it. I get the opportunity to make things better, build relationships with people that I get to tell on a daily basis they did their job wrong, and I get paid for it. I've been fortunate to actually see some of the things I've worked on in my life get sold for profit, and I've seen some shelved for reasons that only the deity of your choice knows why. It is satisfying for me to see my product and efforts be successful and allow other people to make a difference, learn something new, or make a living from it.
This about does it for my first blog post. If you've gottent this far, thank you for reading my whole post. Please stay tuned for more rambling thoughts from a depressive nymphomaniacal insomniac. And remember, you always have a choice. You may not like all of the options, but you always have a choice.
Affectionately yours. Gio
posted by Juan Giovanni at 11:00 PM
1 Comments:
ya, (a+b)x(a-b)=a^2-b^2.
This is a very common and handy formula. In your case, you have made a specific usage of it, wherein you have defined a=b+1. Therefore, a-b remains 1 and leaves the formula in a very simple and amazing form of a^2-b^2=a+b.
Congratulations for realising that at the age of nine! Nine is a fantastic number for me! My memory being weak, i was horrible at mathematical tables in school, except 9, which i loved to work out while chanting! Hope you understand me!
Ever heard of an Indian lady named Shakuntala Devi? She is fantastic with numbers...I got some inspiration from her. Do check her out through Google!
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