point in math
- Thread starter Ryan$
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Hi guys!
I know what the definition of derivative , it's like this : in geometry if I have a volume with specific function that's demonstrate the volume in the plane, then if I have do derivative to the function I get the value of the point in that volume!
Well, another something is confusing me ! and yeah lemme close this gap and you guys already know me and you already helped me in math alot! last thing left and all understandable in aspect of point in math.
if you claim that point has nothing ..I'm totally with you ! then if I have a function F(x) , and I assign x=0 , then at F(0) I've a value ! and we know that x=0 is describing a point in math! like 0---------------5-------------------7----------------8 , so if we assign a point into F and we get a value this means that point has a value ! then it's opposite to what you told me guys ! "one again I'm wrong but I need to be convinced .. I can't solve without convince! sorry !!!
I know what the definition of derivative , it's like this : in geometry if I have a volume with specific function that's demonstrate the volume in the plane, then if I have do derivative to the function I get the value of the point in that volume!
Well, another something is confusing me ! and yeah lemme close this gap and you guys already know me and you already helped me in math alot! last thing left and all understandable in aspect of point in math.
if you claim that point has nothing ..I'm totally with you ! then if I have a function F(x) , and I assign x=0 , then at F(0) I've a value ! and we know that x=0 is describing a point in math! like 0---------------5-------------------7----------------8 , so if we assign a point into F and we get a value this means that point has a value ! then it's opposite to what you told me guys ! "one again I'm wrong but I need to be convinced .. I can't solve without convince! sorry !!!
but help me to understand
! that's why I need to learn .you said that point has nothing, no value , it's just a point , nothing more nothing else ! I'm fine with this.
but lets assume x=0, and I have a function which it's describing F(x) in a place ,, then F(0) has a value that's means x=0 has a value that's means a point has a value ! that's opposite to what you told me !
the definition of derivative is describing the value for every x by d(fx)/dx ...
but I already asked above something else ,, may please please answer it? after "well ...................... "
No one said (FIND IT) that a point has no value. You made that up. A point on the number line has a value. The point representing zero has the numeric value of zero. If f(0) exists, it may (and usually will) have a value different from 0. f(x) does not determine x; rather x determines f(x).but help me to understand
you said that point has nothing, no value , it's just a point , nothing more nothing else ! I'm fine with this.
but lets assume x=0, and I have a function which it's describing F(x) in a place ,, then F(0) has a value that's means x=0 has a value that's means a point has a value ! that's opposite to what you told me !
may you explain more? it's exactly my gap! really not kidding !
didn't understand your answer ..how point has value once and in other hand you told me it's as no value
maybe an analogy would be fantastic ! thank alot
if F(x) !=0 that means that point has a value ! .. in the other thread told me that point doesn't have a value ...so?!
I promise that would be last thing about point ... really that's my gap!!
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I was after something like:
[MATH]\frac{d}{dx}f(x)\equiv\lim_{\Delta x\to0}\frac{f(x+\Delta x)-f(x)}{\Delta x}[/MATH]
There is a subtle difference between a point and an interval whose width is approaching zero. You need to study limits first before tackling the derivative.
A point on the number line represents a numeric value. Neither I nor anyone else said that a point on the number line has no value. Link to where anyone whatsoever said that.
What you are probably remembering is that in geometry, which is the study of an idealized space, a point has neither height, width, or depth. What is the height of a number? What is the width of a number? What is the depth of a number?
One reason that we can translate arithmetic into a geometric analogy is that neither numbers nor the idealized point of geometry have breadth, height, or depth. That does not mean that a number has no numeric value. And if we associate a point with a number, then that point represents a numeric value.
What you are probably remembering is that in geometry, which is the study of an idealized space, a point has neither height, width, or depth. What is the height of a number? What is the width of a number? What is the depth of a number?
One reason that we can translate arithmetic into a geometric analogy is that neither numbers nor the idealized point of geometry have breadth, height, or depth. That does not mean that a number has no numeric value. And if we associate a point with a number, then that point represents a numeric value.
because we can representing a point by a number ... it means has a value .. no?! isn't a representation means the a point has a value?!
I mean if point represent 5 .. so point has a value of 5 no?! so point has a value no?
It is perhaps a little sloppy to say that a representation of something is that something. But yes a point on the number line can have a value. NO ONE SAID IT CANNOT. You simply made that nonsense up.
but once again if it has a value , then if we do distances like 5------------6--------7 , 6-5=1, 7-6-epsolon = distance between 7-6, so all distance is
(6-5)+(7-6-epsilon)
why I say that? because you said now that point has a value, so if it has value then I must wipe it off in the second calculation of distance to calculate all the distance .. but you already told me that it's wrong because point has no value and no need to consider epsilon
-epsilon is because we have already said that a point has a value and point of number 6 is calculated twice in calculating the all distance between 5---7 !
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A point has a location, and we may decide to assign that location a coordinate which can stand for the value associated with the point, But again, the point is a dimensionless entity, it does not have a width of \(\epsilon\) or any other non-zero value you're trying again to assign to it.
you mean representation doesn't mean that a point has a width? and the number we associate to the point doesn't mean that it has an entity's value?
I'm totally with you ... but if it has a location as numbers ..doesn't mean it has a size/value of its entity?!
in brief.. how can I imagine a point while solving and avoid the confusing things about point ?! like what I have been asked in this thread .. I want a good analogy to imagine it by solving to overcome on that confusing things!
maybe help me please? thanks alot
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You're not with me at all if you continue to insist that a location implies a size. These are two independent attributes.
You do manage to confuse the simplest things.
[MATH]7 - 5 = 2.[/MATH]
If you do not believe me, put seven pennies on a tabletop. Count them very carefully. Now take five away. Make sure that you really have taken five away. Now count how many pennies are left on the tabletop. Count them very carefully. You will find that there are exactly two pennies left.
Now it is true that we can go as follows
[MATH]2 = 7 - 5 = 7 - 5 + 0 = 7 - 5 + 6 - 6 = (7 - 6) + (6 - 5) = 1 + 1 = 2.[/MATH]
But we did not add 6 twice. Nor did we subtract 6 twice. We added 6 and subtracted 6.
There is no [MATH]\epsilon[/MATH] involved. Again, that is some nonsense you made up.
The analogy is what is confusing you. You can do all of algebra and calculus without reference to geometry. Analytic geometry is an analogy between numbers and points. If the analogy confuses you, forget about it.