the A,B busness was a bad analogy, i'm sorry.
my point is that we can define 0/0 in a given instance, and that in every instance, there is one and only one possible value we can define 0/0 as, and that value is always a real number. we can not assigne a spicific value to 0/0 for any case, the way we can with 2/4 or 1/3, but i bet that we can make some rules about how 0/0 changes in acordance with the case in question.
unfortenetly, it seems that all i've actualy done here is proven the prosses of "plugging the gap" of a removable discontinity to be a viable way of dealing with certain point discontinuiteies. however, my argument is inconclusiv because it's keystone is the very prosses it is trying to validate.
given that, i'm inclined to agree with odvious overture.
Originally posted by TheMaster37exactly 0/0 does not mean anything, it is an impossible mathematical statement. if you take the limit of sinx/x as x goes to zero you get 1. however that does not mean sin0/0 equals 1. rather the limit of the number approaches 1 but at 0 you have an indeterminate number which means nothing at all.
Sorry, but i fail to see how a statement can be true AND false at the same time in any situation.
And apologies again for not seeing how statement A can be true OR false. Assuming either one leads to a contradiction in the argument, so statement A is neither true or false.
Our argument is; no matter what you choose for 0/0 to be, it will always lead to discussions, since no single number can be chosen to that 0/0 has a sensible meaning.
Originally posted by TheMaster37explain how 0^0 woldn't = 1.
Said more nicely:
If you look at the function sin(x)/x, you WANT 0/0 to equal 1.
If you look at x^0 you WANT 0^0 to be 1
If you look at 0^x you WANT 0^0 to be 0
That is all that limit means; what you WANT the function to be in that point to the entire function "behaves good"
Originally posted by TheMaster37That isn't what a limit is at all. That's a brutal explanation - kids, don't listen to him, he's the devil.
Said more nicely:
If you look at the function sin(x)/x, you WANT 0/0 to equal 1.
If you look at x^0 you WANT 0^0 to be 1
If you look at 0^x you WANT 0^0 to be 0
That is all that limit means; what you WANT the function to be in that point to the entire function "behaves good"
If I WANT the limit of f(x)=1 as x approaches 2 to be pi, it doesn't make it pi!
The limit of a function at some point is NOT THE SAME as the value of the function at that point (although they can be equal in value). What you're talking about is defining a function in a piecewise fashion. Limits are an entirely different kettle of fish.
To fearlessleader; Why would it be 1? To make 0^x continuous in every point of it's domain we would have 0^0 equal to 0.
To PBE6: Read better. I said that limits are what we WANT a function to be for it to "behave good"
Define F(x) = sin(x) for x unequal to pi/2 in the interval [0, pi). Define F(pi/2)=0
What we WANT F(1) to be to make the function F "pretty" is F(pi/2)=1.
That is EXACTLY what lim F(x) is for x -> pi/2
PBE6, TheMaster37 is talking about making functions continuous; f is continuous at a iff lim(x-->a)f(x) = f(a). You're quite right, a function does not in general have this property, but the whole point of this thread is that 0/0 is indeterminate but we can make a function that takes the value 0/0 at some point behave nicely by defining its value at that point by a limit.
TheMaster37, are you joking? You don't understand the first thing about limits, you can't write with proper grammar, spelling, syntax, or even flair, and yet you have the gall to tell me to read your last post "better"? OK you little urchin, let's re-read your last post together:
To PBE6: Read better. I said that limits are what we WANT a function to be for it to "behave good"
Well, you got me there. You did say that, didn't you? Too bad it's wrong.
Define F(x) = sin(x) for x unequal to pi/2 in the interval [0, pi). Define F(pi/2)=0
What we WANT F(1) to be to make the function F "pretty" is F(pi/2)=1.
That is EXACTLY what lim F(x) is for x -> pi/2
The limit of F(x) as x approaches pi/2 is indeed 1, but not because you WANT it to be. It didn't work when you WANTED to impress that cute girl in the mini-skirt, it didn't work when you WANTED to dunk like Jordan, and it's not going to work here.
Firstly, this statement doesn't make sense:
What we WANT F(1) to be to make the function F "pretty" is F(pi/2)=1.
Secondly, when you say a function "behaves good", you're butchering the English language. Shape up.
Thirdly, I think F(x) looks "prettier" with a round hole indicating a discontinuity at x=pi/2, with the missing point floating about 8 inches above it. It's like a beauty mark. Can I make the limit 1 + 8 inches? Of course not. That's completely inane. Just like your definition of a limit. Try applying it to f(x)=x^x as x approaches 0. You'll find that although the right-hand limit exists, the left-hand limit does not, indicating that there is no limit proper. But 1 would look "pretty" according to your aesthetic sense, wouldn't it? Rubbish.
So there you have it. Just say what you mean next time, and take the time to check it over before challenging your critics.
Originally posted by royalchickenOh, I know what he was trying to say. He just never actually said it - and what he did say was just plain wrong.
PBE6, TheMaster37 is talking about making functions continuous; f is continuous at a iff lim(x-->a)f(x) = f(a). You're quite right, a function does not in general have this property, but the whole point of this thread is that 0/0 is indeterminate but we can make a function that takes the value 0/0 at some point behave nicely by defining its value at that point by a limit.
Originally posted by TheMaster37prehaps the limit of 0^x as x->0=0, but why should 0^x be continues?
To fearlessleader; Why would it be 1? To make 0^x continuous in every point of it's domain we would have 0^0 equal to 0.
it seems clear to me that with no 0s being mulitiplied, all you would have is 1. same as any other number^0
and dont argue that 0^x should be continus on the basis that other number^x functions are continus. just look at -1^x.
Originally posted by PBE6You've just proven yourself to be a complete and utter pain the the rear-end (I'll refrain from stronger language in fear of moderation).
TheMaster37, are you joking? You don't understand the first thing about limits, you can't write with proper grammar, spelling, syntax, or even flair, and yet you have the gall to tell me to read your last post "better"? OK you little urc ...[text shortened]... nd take the time to check it over before challenging your critics.
I never said that limits are DEFINED by what you want them to be. I was merely trying to EXPLAIN what a limit means in non-mathematical language, with that everything i said is still true
Basically, if you assume that "behaves good" means having a hole in your function then you are the strange one. If you think holes are beautifull, then define a new limit-process and enjoy yourself with it somewhere else. Assuming you have a brain, i would have thought you'd use it, and see that with "behaves good" i couldn't mean anything else but continous. Even more so when you consider that my posts were directed at non-mathematicians, who have no idea what "behaves good" can mean besides being able to draw the graph with a single stroke of the pen. (I know i'm in conversation with other mathematicians, but i try not to scare others away with our posts)
Who ever said my native language was english? Even if it was, who says i need flair to write posts?
Yes, i had the nerve to tell you to read better, since obviously, you're not.
Lastly, just to set things straight, i'm a fifth year math student, not too far away from earning his MD.
You've just proven yourself to be a complete and utter pain the the rear-end (I'll refrain from stronger language in fear of moderation).
Just wait, I've got lots more proof.
I never said that limits are DEFINED by what you want them to be. I was merely trying to EXPLAIN what a limit means in non-mathematical language
Fair enough.
with that everything i said is still true
C'mon. It's not even close.
Basically, if you assume that "behaves good" means having a hole in your function then you are the strange one.
What is this, a PTA meeting? Who are you to decide what "good behaviour" is? If the function takes on the value it is defined to take on at all points, then it's well behaved. If the value happens to be "no value" because there's a discontinuity, so be it. End of story.
(royalchicken, I know he means "continuity" when he says "good behaviour". Why can't he just say it without attaching all sorts of value judgements?)
If you think holes are beautifull (sic), then define a new limit-process and enjoy yourself with it somewhere else.
What I said was:
I think F(x) looks "prettier" with a round hole indicating a discontinuity at x=pi/2, with the missing point floating about 8 inches above it. It's like a beauty mark.
What you said about holes was very Freudian. Please deal with those issues in another thread. Now, didn't you just say that you never DEFINED the limit of a function to be the value we "want" it to be? Let's check:
I never said that limits are DEFINED by what you want them to be.
Yep, you did. So why would I have to:
define a new limit-process to make discontinuities beautifull (sic)? Did you accidentally redefine something when you weren't looking? The definition I'm using, also known as the correct one, works just fine for all curve, regardless of the number of discontinuities.
Assuming you have a brain, i would have thought you'd use it
Where did you pick that one up? Playing with you nephew's Tonkas in the sandbox? Wrestling with babies? I think I've heard snappier comebacks at the morgue.
and see that with "behaves good" i couldn't mean anything else but continous.
It's "behaves well"..."behaves WELL". "Good" is an adjective, "well" is an adverb. "Well" modifies the verb "behaves" in this sentence. If your sentence had meaning, we'd have something to talk about.
Even more so when you consider that my posts were directed at non-mathematicians, who have no idea what "behaves good" can mean besides being able to draw the graph with a single stroke of the pen.
Just because you consider your audience beneath you, there's no reason to lie to them.
Who ever said my native language was english? Even if it was, who says i need flair to write posts?
I was searching for something nice to say that would redeem the content of your posts. I came up goose-eggs.
Yes, i had the nerve to tell you to read better, since obviously, you're not.
I'm not what? A "read better"? Let me read that again.
Yes, i had the nerve to tell you to read better, since obviously, you're not.
Hmm. Alright, you got me on that one. Your post is impenetrable. I'll read gooder next time, I swears.
Lastly, just to set things straight, i'm a fifth year math student, not too far away from earning his MD.
I think you're getting further away with every post.
(Just kidding, good luck with your Master's studies.)
Originally posted by PBE6Ok, I agree the grammar has some room for improvement. Let's just say I'm better at it when I take the time to check what I've written just now :p
[b]You've just proven yourself to be a complete and utter pain the the rear-end (I'll refrain from stronger language in fear of moderation).
Just wait, I've got lots more proof.
I never said that limits are DEFINED by what you want them to be. I was merely trying to EXPLAIN what a limit means in non-mathematical language
Fair enough.
[ ...[text shortened]... etting further away with every post.
(Just kidding, good luck with your Master's studies.)
[/b]
When I said "behaves good" (That's what I've been saying so I won't pretend I did it right in the past posts) I was adressing a non-mathematical audience. They have no idea what continuity means, and will most likely run away when I throw in some epsilons and deltas. I don't bother them with the formal definition, I'm merely trying to create a picture to go with all our mathematical babbeling.
I'm sure you realise that most people without advanced mathematical education will find a discontinuity strange/ugly/whatever. If we take the example I gave earlier;
F(Pi/2) is a discontinuity, using my earlier words: In order for this function to "behave good" (meaning nothing else then continuous wich was quite obvious from the context, especially when I pointed out that I was adressing non-mathematicians) we want F(Pi/2) to be 1. Assigning that value nicely gets rid of the hole, and we can draw the graph with a single pen-stroke again.
I am quite confident that I didn't say anything untrue in my posts, and re-reading your posts I see that the only thing you do is pointing out that I'm lying. So far, you haven't quoted a single line that is untrue. Ok, my choice of words is unfortunate at times, but after reading this post you surely must see that what I said is no lie.
(And I hope the english in this post is much better than in my previous posts. I didn't re-read my post to correct things, so it might still be less than perfect)
Originally posted by TheMaster37TheMaster37, you seem like a stand-up guy. The seed that started this whole thing was the following statement from your Nov. 23 post:
Ok, I agree the grammar has some room for improvement. Let's just say I'm better at it when I take the time to check what I've written just now :p
When I said "behaves good" (That's what I've been saying so I won't pretend I did it right in the past posts) I was adressing a non-mathematical audience. They have no idea what continuity means, an ...[text shortened]... ious posts. I didn't re-read my post to correct things, so it might still be less than perfect)
That is all that limit means; what you WANT the function to be in that point to the entire function "behaves good"
I still say that's wrong. But I understand why you said it that way. Kudos to you for trying to enlighten the mathematically challenged.
Now, back to slagging random folk.