Dear J-Lo,
I almost called you Jello, but given the language/cultural divide between us, I wasn?t sure you?d understand that I was implying you had gelatin for brains. So I?ll leave it with a pop reference you can probably manage.
Where do I begin? First off, I?d like to say you?re spectacularly unique here at this forum. I?ve read hundreds and hundreds of posts, and yours stand out as the most painful to read. I mean, when someone takes so much time to be so very wrong, where do the rest of us even begin???
So I?ll start with the niceties. I understand your perspective. English is not your primary language, and it is unlikely you would ever have read a Calculus text in English. So rather than lambasting you for that, let me clear up a few vocabulary problems first.
Ok?mathematical modeling: We use graphs to model functions and equations. It helps us analyze problems on paper that are vastly too complex to analyze in real world terms. Calculus, actually, was invented specifically to describe the arc a projectile follows after launching it. Like many scientific advances, Calculus was inspired by the need for better warfare.
The simplest mathematical model is a one-dimensional coordinate system called (in English, at any rate), a number line. It?s a straight line. Zero is assigned somewhere along it arbitrarily, and unit distances (-3,-2,-1,0,1,2,3) are picked and written along this line. One the line, meaning in the model, numbers approach. You approach zero. Or you approach a different point along the number line.
You are partially correct. Numbers are what they are. But in a function, the function ?approaches? certain solutions, including the limit.
So please do forgive me for using English in my post. But had you actually read the post instead of rushing in limp-brained to insult someone, you would have noticed that my first two sentences were, ?Vaxer, 0.99999999 never equals 1. But as you look further and further past the decimal point, it begins to approach 1.? I can see how your ESL take on things would misinterpret that to mean the numbers jumped into a Ferrari and zoomed along a freeway. Again, I can only apologize for my native tongue and forgive you for never having studied math in an English classroom.
But think about what I said again. I know it hurts your brain. You hate reading what others post before insulting them. But try. Pretty please?
I said that as you look further and further past the decimal point, the number approaches 1. The number 0.9 (think 90%) is a lot closer to 1 than the number 0.99 (think 99%). So, as I indicated, the further past the decimal point (on a number line) you go, the more the decimal approaches 1.
Does that clarify your confusion? I hope so. Let me know if it doesn?t, and I?ll see about hiring you a tutor. I hear that many twelve year olds in your country can understand this much. I?m sure they work cheap.
You wrote,
numbers don't move. that's what we all should know and this pretty much is the reason why all you say is plain wrong - even if at first glimpse this might seem to be hairsplitting. i am very well aware of what you mean and it's plain wrong.
as we now agree that numbers don't move, they can't approach each other. so the number 0.(9) (meaning 0.9999999... ad infinitum) doesn't approach 1. it either IS 1 or there is a difference between them. a number doesn't change depending on how far you look beyond the decimal point. the number 0.(9) exists as a whole number of infinite decimals and it doesn't give a crap for how far you please to look.
Do you think, now, that you might want to recant that position? Pure mathematics is different from the real world. But as we can all probably agree, Calculus was created for, and continues to exist for, measuring real-world situations too complex to measure without a simplified model. But again, I?m talking about the difference between 0.9, 0.99, and 0.9999999999999999999. Depending on where you choose to cut off your decimal places, the number does actually get a lot closer to 1 the further along the number line you go.
It perplexes me that you chose to include a bastardized version of Zeno?s Paradox (the turtle story). It doesn?t really support your point at all.
In the Paradox, yes, there is a point where the runner and the turtle?s points converge. And yes, that is the ?limit.? But there is a fundamental error in Zeno?s reasoning. It assumes an infinite amount of time is used to cover a distance divided into infinite numbers of segments. So Zeno?s setup was flawed from the beginning. I?m not sure how that particular image furthered our discussion here, but then again, most of your writing is flawed. Perhaps I shouldn?t be so shocked.
Oh, I just looked at your post again. I thought I should clarify. In English, Calculus is referred to as Integral, not infinitesimal.
But back to my original meaning in my previous post: One never equals 0.999999999?But in certain functions (abstract mathematical functions and graphs), it is important to know what happens really really close to the point on the graph where .999999 would either become 1 or would be undefined.
In simple real world situations, such as determining how much gasoline is consumed per hour at different speeds and elevations, treating 0.99 and 1.0 as equal might not be a big problem. But if you?re trying to land a $3 billion probe on a different planet, you?d better not round your numbers off to the second decimal place.
And Jay, for goodness sake, could you please stop posing as a smart man? You may be bright, but reading your posts over the last month, I can?t say they reflect that very well. You are so quick to jump in and attack others that you often forget to read through your own posts to make sure they are logical, ordered, and true.
IN this last case, you moved so quickly that you forgot to read my first sentence. Then you called me an idiot and turned around and asserted the very same thing. Remember, writing a lot of words poorly is never a substitute for clear thinking.
Also, for everyone else, I did actually write, ?Anyway, it's been fifteen years since I picked up a calculus book, so correct me if I'm wrong!!!? I was just trying to join in on a discussion, and I was humble enough to admit my own limits. Wow, I didn?t even need Calculus for that!