Just imagine if the Economics Teacher in Ferris Bueller's Day Off would have said: "Any.99999999999999999999999999999999999999999999999999999999999999999999999999999...??? Any.99999999999999999999999999999999999999999999999999999999999999999999999999999...???" Or, if Doc Brown says: " .999999999999999999999999999999999999999999999999999 point twenty .999999999999999999999999999999999999999999999999999 jigowatts of electricity!!!"
please read this article. pay attention to item #3 and #5 http://www.cracked.com/blog/5-popular-jokes-that-only-make-people-want-to-punch-you/
What this really means is that occupy wall street was all for naught since the 1% is just as part of the 99%
I don't think jewelers will buy that when you say you should get the price of a X.0 carat diamond at the price of the X-1.9999999 repeating diamond b/c it's the same thing.
I haven't used any math above an elementary level since I graduated. Gotta love calculators, excel, and online tools.
Using addition or multiplication rules is a common way of showing .999... = 1 but somewhat misses the point. In mathematics, there are many ways of trying to think about numbers. Mathematicians set up basic rules for a system, called axioms, and see what kind patterns and conclusions can arise from playing with this system. Here's a somewhat real-world thought experiment (not exactly synonymous with the .999... stuff): When you think of 1 apple, what defines a singular apple? It has certain qualities it shares with other "apples" such as color, texture, parts, taste, smell, composition, growth, etc.. but by no means is it the same as any other apple in the world. It is also constantly breathing, decaying, and changing, and sharing molecues with everything around it. Where does the apple begin and where does it end? In the same way, mathematicians see units like the number 1, and are ask "how can we represent numbers in the most "natural-to-the-universe" way, so when we play around with the axioms and system, we are most likely to discover significant truths and conclusions?" The number 1, if you think about it, is a very weird concept, which signifies an exact border between two entities. This is where mathematicians come up with ways of representing numbers like Dedekind cuts: http://en.wikipedia.org/wiki/Dedekind_cut A "cut" is basically when all the stuff before the cut is less than anything after the cut. There is also no maximum value of stuff before the cut, so even if you have .999, you will always have .9991, then .9992, and so on an so forth and be closer and closer to 1. If these properties are satisfied, then you have a cut, in other words a rational number. Dedekind cuts might seem weird at first, but you'll find that the way we think of numbers is somewhat artificial and fabricated (yet extremely useful for practical use). Dedekind cuts are counter-intuitive but a "natural" way of explaining what a number is. The reason .999.. is equivalent to 1, is because there exists no element greater than .999... Both .999... and 1 satisfy the same properties and thus are the same cut. That's just one way of thinking about objects (numbers), rules, and systems. Dedekind cuts are extremely useful when talking about systems where distance has no importance, such as topology. Anyways, a look into a mathematician's mind.
Technically, if you drop an egg from, say, three feet above the floor, it should never actually HIT the floor. Because, you can continue to divide the remaining difference by half into infinity. It falls 1.5 feet, still has 1.5 feet to go, then .75 feet, etc etc etc, so on and so on, to an infinite number of divisions, meaning that the egg should never hit the floor. Obviously, while this may be technically true, the reality is that you have a mess to clean up because the egg doesn't care what kind of ridiculous math problems you are doing in your head - the real world works the way it always has, and will continue to do so. In the same way, the number '1' will remain being the number '1', regardless of whether or not someone comes along and says differently. As Shakespeare indicated: you can call a rose something other than a rose, but it is still going to smell like a rose, because that is what it IS.
This (and other variants of Zeno's paradox) is just a flaw in mathematical reasoning. What this guy is saying is not similar to that. I think his point is more philosophical (what are "numbers" and in what sense do they exist in the real world) rather than a mathematical assertion.
Both numbers and math are a language. It's all about language. They exists to explain things, to talk about the world. They are not things themselves. So, when a mathmatician is forced to say ".999..." is the same as 1...it's like "OK, dude, whatever fits your world of talking about fractions." If he doesn't say they are equal, then his language breaks down. I have no problem with this, because a Point must not have any width...thus, there are an infinite amount of points on any line. It's is just a definition of ideas that allow the idea of Math to work. And, yes, I'm completely serious about this.
