point in math

Ryan$ said:
to sum up your words, you mean that the imaginary world is perfectly ideally concrete and we should visualize thing like this.
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The imaginary world is ideal, and your problem does not arise there. The concrete world may or may not match the ideal world exactly, but it matches so closely that we cannot measure the difference.

To put it slightly differently, we can use Euclidean plane geometry for problems involving a small enough area and never notice the difference even though we know that the surface of the earth is not a Euclidean plane.
 
JeffM said:
The imaginary world is ideal, and your problem does not arise there. The concrete world may or may not match the ideal world exactly, but it matches so closely that we cannot measure the difference.

To put it slightly differently, we can use Euclidean plane geometry for problems involving a small enough area and never notice the difference even though we know that the surface of the earth is not a Euclidean plane.
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I got you, so lets assume I have 2------------5 and I want the distance between them ; I do 5-2 =3 ; but my question is "2" included in calculation of the distance between 2---5 or not?
 
Ryan$ said:
I got you, so lets assume I have 2------------5 and I want the distance between them ; I do 5-2 =3 ; but my question is "2" included in calculation of the distance between 2---5 or not?
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xxxxx

Take xx away.

You have xxx left.

You keep going back to this idea that it is helpful to view 2 as something that exists only as some accumulation of numeric atoms. That idea is not helpful.

Do you REALLY believe that if you have have five shrimp and you give to 2 a friend that you will have something different than 3 shrimp for yourself?

Of course you do not. So why do you persist in a train of reasoning that makes you doubt that taking 2 shrimp from a set of 5 shrimp might not leave 3 shrimp remaining?

I explained this several posts ago. You can either agree that thinking that 2 exists only as the sum of whole bunch of numeric atoms is not helpful, or study analysis, either standard or non-standard. Non-standard is closest to your train of thought that 2 is a valid concept only if it is the sum of a numeric atoms.
 
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Ryan$ said:
Japanese, yeah , but why are you asking that question?
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Because you should be talking to someone at the university of Tokyo or Kyoto so that there is less of a language barrier. It is very difficult to explain subtle concepts when neither party is good at the other's language. I do not think that we have anyone here who speaks Japanese.
 
JeffM said:
xxxxx

Take xx away.

You have xxx left.

You keep going back to this idea that it is helpful to view 2 as something that exists only as some accumulation of numeric atoms. That idea is not helpful.

Do you REALLY believe that if you have have five shrimp and you give to 2 a friend that you will have something different than 3 shrimp for yourself?

Of course you do not. So why do you persist in a train of reasoning that makes you doubt that taking 2 shrimp from a set of 5 shrimp might not leave 3 shrimp remaining?

I explained this several posts ago. You can either agree that thinking that 2 exists only as the sum of whole bunch of numeric atoms is not helpful, or study analysis, either standard or non-standard. Non-standard is closest to your train of thought that 2 is a valid concept only if it is the sum of a numeric atoms.
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thanks!! I appreciate your effort on answering me !
 
Hi , I know that I already opened this thread before but I really want to understand and to get the idea behind of the terms quantity.
I attached a photo which is explaining everything, from point a to b there's quantity 5, from b to c there's quantity 6, at the point itself there's no quantity and I understand that but what's still confusing me, lets assume that 5 is representing 5 potato which are scattered from point a to b, and 6 potato are scattered from point b to c, who said if I go from point c to any point which exceeds the point b then the area which are passed from point b to the point that I exceeded by (( I mean the black area that I colored in the photo where is the "?" ) then I will count any potato in that area? maybe that all five potato which are scattered from point a to b are scattered in away excluded the area of "?" then the area of "?" nullity and there's no quantity in it .. so why we are consider that area of "?" as quantity ?! who said in that area "?"(see the photo) will be potato?! ofcourse potato are scattered from point a to b but none confirms that there in that area "?" will be potato .. any help please to illustrate that thing? I'M VERY CONFUSED in that thing how area actually representing a quantity .. is that theory in math?! thanks!!
maybe that area (( see where is "?" )) not including potato .. so how we are consider it as quantity?! and if we have area then it's represented a quantity ?!

thanks
 

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Who makes such a claim? I don't know of anybody who would say that if potatoes are scattered within a region, the area of a part of that region would be necessarily related to the number of potatoes there.

Area would only be proportional to the quantity of potato in a region if the potatoes were mashed and spread out with uniform thickness. This is the difference between discrete (individual potatoes) and continuous (mashed potato) quantities. You can't ignore that difference.
 
Dr.Peterson said:
Who makes such a claim? I don't know of anybody who would say that if potatoes are scattered within a region, the area of a part of that region would be necessarily related to the number of potatoes there.

Area would only be proportional to the quantity of potato in a region if the potatoes were mashed and spread out with uniform thickness. This is the difference between discrete (individual potatoes) and continuous (mashed potato) quantities. You can't ignore that difference.
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so point in discrete is not meaning less and not can say about it as "nullity"?! but in continuous yes?
 
You could say it that way. A discrete quantity might represent the location of the center of mass of a potato, so that it can be counted as 1, though the area or volume of a point is zero. In a continuous distribution like the mashed potato, you have to consider some extended region to get a nonzero quantity.
 
Dr.Peterson said:
though the area or volume of a point is zero. In a continuous distribution like the mashed potato, you have to consider some extended region to get a nonzero quantity.
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What do you mean by this? Is point at discrete is also zero?!
 
I thought you were getting the idea.

In a discrete context (such as describing a set of distinct points), we don't care about area or volume, so we wouldn't say that a point is "zero". A point is simply a point -- a location. We can just count points: point 1, point 2, point 3. There is no zero there; each point adds 1 to the count.

In a continuous context, we might be concerned about the volume of, say, an actual potato, which is spread out over some region (the interior of its skin). Then individual points don't contribute anything.

In each case, we are talking about different kinds of things; we only raise questions that are relevant to what we are doing.Your difficulty is in trying to mix different contexts.
 
Dr.Peterson said:
I thought you were getting the idea.

In a discrete context (such as describing a set of distinct points), we don't care about area or volume, so we wouldn't say that a point is "zero". A point is simply a point -- a location. We can just count points: point 1, point 2, point 3. There is no zero there; each point adds 1 to the count.

In a continuous context, we might be concerned about the volume of, say, an actual potato, which is spread out over some region (the interior of its skin). Then individual points don't contribute anything.

In each case, we are talking about different kinds of things; we only raise questions that are relevant to what we are doing.Your difficulty is in trying to mix different contexts.
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Alright you are making my diffculties easier to solve it; so I can assume 90% of our solutions /life rrlated to continues context? Guess so .. Otherwise if we are working in discrete displine in work or something like that
 
I'm not really sure what you are saying. It doesn't appear to be anything I have said. I have no idea whether continuous or discrete problems are more common, and it doesn't matter.

When you solve a problem, just do what makes sense in that problem. Don't worry about irrelevancies.
 
Dr.Peterson said:
I'm not really sure what you are saying. It doesn't appear to be anything I have said. I have no idea whether continuous or discrete problems are more common, and it doesn't matter.

When you solve a problem, just do what makes sense in that problem. Don't worry about irrelevancies.
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Alright ! very good illustration I would like to thank you very much on your explanations!
 
To be more assure and close this gap. so we have two context one is discrete and other is continuous, related to my example that I attached above where there's a region "?" it's really matter if we are looking or talking about continuous because it implies an amount in world of continuous and why it imply an amount? because it's like a distance which counted as "amount of" ...
but in world of discrete as what you said not really matter ....

I hope what I said is right /// thanks!
 
Hi guys, I have to confusions which please illustrate for me them in a simple manner.
first is there more than smaller to the point? I mean if I imagine a point .. then I can also imagine a point inside the point that I imagined which it's smaller than what I imagined .. so?

second question, is continuous function means that at everypoint there's a possibility that the values of function over it will be changed? thanks alot

and who said that at every point I have value? maybe at semi-point I have value? who corresponded that a value corresponded to a point and not to semi-point?! thanks alot
 
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No, if you correctly imagine a point, then you can't imagine anything smaller! A point is to be thought of as a mere location, with no size at all. Yes, it's hard to imagine that; but if you imagine a size, then you are imagining wrongly, just as you would be wrong to imagine a vacuum from which you could suck more air than you already did to form it.

As for functions, a function isn't something that changes; it is a particular relationship between an input and an output. For any give input, the output is fixed. So it's not at all clear what you are thinking. A continuous function (leaving out some technical details) is one whose graph can be drawn in one continuous line, without ever lifting your pencil. It has to do with how values of x close to one another affect values of y -- if x doesn't change much, y shouldn't change much. (You need calculus to really express this correctly.)
 
Wow convinced me about point in away that I cant say anything :) ?
Another thing then why we assume that value is corresponded to a point and not for example a value corresponded to semi-point? I mean maybe value occupy two points at one time? Who claims that value number is corresponded to one point at a time?
 
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