Report, edit, etc...Posted by CheeZe on 2005-09-11 at 15:09:25
Where's your source? Because I'm getting all of my information out of my textbook and other sources like my hand book... definition... and friend. 
Report, edit, etc...Posted by DT_Battlekruser on 2005-09-11 at 15:33:42
The actual definition of limit states
"L=lim[sub]x→c[/sub] f(x) if and only if for any number ε>0, there is a number δ>0 such that if x is within δ units of c (but x ≠ c), then f(x) is within ε units of L."
This actually returns to the infinity conundrum, because lim[sub]x→2[/sub] l1/(x-2)l is a case where δ and ε go to infinity. There is a problem in my book which contains such a function, and their answer is to state that the function has no limit.
Also, in section 2-5 "Limits Involving Infinity", the author states
"The = in mathematics is used to connect two equal numbers. Because infinity is not a real number, it is more appropriate to say 'the limit of f(x) is infinite' rather than saying 'it equals infinity'. Sometimes, when it is important to describe briefly the direction in which a function goes to infinity, the following statements are used.
lim[sub]x→c[/sub] f(x) = ∞ or lim[sub]x→c[/sub] f(x) = -∞
The symbols ∞ and -∞ are convienent shorthand for describing the behavior of the function at x=c. You should realise the the limits still do not exist. The notation simply explains why the limits do not exist. They are undefined because they are infinite. Note that a limit may be undefined without being infinite. For instance, the limit of f(x) = lxl/x as x→0 is undefined because of a step discontinuity there.
The statement x→∞ is also somewhat misleading. Although pronounced 'x approaches infinity', the statement really means 'x gets infinitely far away from zero'. No matter how large x gets, it can never be close to infinity!"
Source: Calculus: Concepts and Applications, Paul A. Forester
One may say the matter could be debateable.
"L=lim[sub]x→c[/sub] f(x) if and only if for any number ε>0, there is a number δ>0 such that if x is within δ units of c (but x ≠ c), then f(x) is within ε units of L."
This actually returns to the infinity conundrum, because lim[sub]x→2[/sub] l1/(x-2)l is a case where δ and ε go to infinity. There is a problem in my book which contains such a function, and their answer is to state that the function has no limit.
Also, in section 2-5 "Limits Involving Infinity", the author states
"The = in mathematics is used to connect two equal numbers. Because infinity is not a real number, it is more appropriate to say 'the limit of f(x) is infinite' rather than saying 'it equals infinity'. Sometimes, when it is important to describe briefly the direction in which a function goes to infinity, the following statements are used.
lim[sub]x→c[/sub] f(x) = ∞ or lim[sub]x→c[/sub] f(x) = -∞
The symbols ∞ and -∞ are convienent shorthand for describing the behavior of the function at x=c. You should realise the the limits still do not exist. The notation simply explains why the limits do not exist. They are undefined because they are infinite. Note that a limit may be undefined without being infinite. For instance, the limit of f(x) = lxl/x as x→0 is undefined because of a step discontinuity there.
The statement x→∞ is also somewhat misleading. Although pronounced 'x approaches infinity', the statement really means 'x gets infinitely far away from zero'. No matter how large x gets, it can never be close to infinity!"
Source: Calculus: Concepts and Applications, Paul A. Forester
One may say the matter could be debateable.
Report, edit, etc...Posted by CheeZe on 2005-09-11 at 15:38:05
LoL. I just realized this is the same arguement I had with my teacher. Apparantly, because infinity is not a real number, I'm not allowed to say lim(x-->c)f(x) = infinity, unless I also say, the limit does not exist. 
So, I guess we're both right.
So, I guess we're both right.
Report, edit, etc...Posted by Mr.Kirbycode774 on 2005-09-11 at 21:14:45
lol CheeZe.. yet ANOTHER person in infinity you've made a truce with?
Hitting the exact middle (if possible) will make the pencil rotate at a speed of zero.
You should look at threads I have created. You'll get your answer.
QUOTE(Slyence @ Sep 10 2005, 09:37 AM)
Because if we put something on the disc so it rotates with the disc, and move it closer and closer to the centerpoint, it will eventually stop rotating with the disc and rotate around itself. If it rotates around itself completely, it should be in the exact middle. The problem is, the exact middle will always be smaller than the object itself, thus infinity?
There's a much easier situation to use than this. Take out a ruler and notice the number marks. Do 1, 2, or even 3 inches exist? So supposedly we can never directly "prove" that any given segment is EXACTLY some amount, but does that mean that they don't exist? Carpenters and construction workers would probably give you a funny look if you asked them if "exactly" this length exists.QUOTE
Or even better; if we keep on going to the center of the rotating disc, we will continue to go slower and slower. Thus infinity?
It won't go "infinity slow", but nowhere fast! Hitting the exact middle (if possible) will make the pencil rotate at a speed of zero.
QUOTE
Thus, by these thinkings I think infinity does exist, else things do not make sense. Not even religion. "God did it", "From what did God come?", "He was always there", "Thus infinity".
You should look at threads I have created. You'll get your answer.Report, edit, etc...Posted by CheeZe on 2005-09-11 at 21:21:28
Truce? I still have no idea what you're definition of infinity is, nor what the heck your beliefs actually are.
I didn't make a truce, he didn't explain it the way I understood it so I was thinking of something else. We're both right. Infinity isn't a real number, but the limit exists. The reason he said it didn't was because it isn't a real number.
I didn't make a truce, he didn't explain it the way I understood it so I was thinking of something else. We're both right. Infinity isn't a real number, but the limit exists. The reason he said it didn't was because it isn't a real number.