Quantities in math (If there are no potatoes, does the area become zero?)

Ryan$

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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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Dr.Peterson

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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.
 

Ryan$

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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.
so point in discrete is not meaning less and not can say about it as "nullity"?! but in continuous yes?
 

Dr.Peterson

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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.
 

mmm4444bot

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so point in discrete is not meaning less and not can say about it as "nullity"?
This is garbled English. 💡 Please try using: translate.google.com
 

Ryan$

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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.
What do you mean by this? Is point at discrete is also zero?!
 

Dr.Peterson

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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.
 

Ryan$

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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.
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
 

Dr.Peterson

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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.
 

Ryan$

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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.
Alright ! very good illustration I would like to thank you very much on your explanations!
 

Ryan$

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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!
 
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