# point in math

#### Harry_the_cat

##### Senior Member
A point has no dimension. From your previous posts, it seems you are stuck on the thought that they do.

May I suggest you think of 5 - 4 as:

Put 5 oranges out on your table and take away 4. There's 1 left.

##### Full Member
what I'm trying to say, sometimes I learn something new like point doesn't have dimension etc ... but while solving my mind taking me to the opposite "struggling .. " is that normal thinking process?! or it's something abnormal to me ?!

#### Harry_the_cat

##### Senior Member
I do think you are over-thinking things - although that's not necessarily a bad thing. Definitions are definitions are definitions.

##### Full Member
Hi guys, first of all, I know that I already opened this subject before, but again I want to close that gap, so I believe by you guys I will overcom on that gap.

"point" in math is nothing, in other words doesn't have dimension, so I totally convinced with that ! but my problem is how can I imagine it? I mean if I'm solving a problem and I imagine a points , how can I imagine them? If I would imagine a point then I make it as it has a dimension, so how actually I imagine it? for instance lets take I have distance like this:
1------------------------------20 , and I want to divide it by half , in other words I will put a "point" on the half of that distance in other words 1--------------------*---------------------20 , so I imagine that point which divide the distance by half like this .. but if so then the point "*" has a dimension because as you see in the graph it has dimension ..so how can I imagine it? what's make me harder to understand the point is, how can imagine it and manipulate it on math?! for example I try to imagine a point in a black circle, but if I take a point on he black circle , then the black circle would have a point of "empty-white" so it's also wrong analogues because it makes a point with dimension .. !! any help how can I imagine point over math?

#### Denis

##### Senior Member
Have a pointedly good day Ryan.

#### lev888

##### Full Member
If I would imagine a point then I make it as it has a dimension, so how actually I imagine it? for instance lets take I have distance like this:
1------------------------------20 , and I want to divide it by half , in other words I will put a "point" on the half of that distance in other words 1--------------------*---------------------20 , so I imagine that point which divide the distance by half like this .. but if so then the point "*" has a dimension because as you see in the graph it has dimension ..so how can I imagine it?
If you divided the line into 2 segments 10 each, how long is the "point"? 20 - 10 - 10 = 0.
You can draw the point however you like, it's still 0 size.

#### Otis

##### Senior Member
... I imagine that point which divide the distance by half like this ...

1--------------------*---------------------20

... but if so then the point "*" has a dimension because as you see in the graph it has dimension ...
The * is not the actual point; it is only your representation of it. (Nobody can draw an actual mathematical point because it's not a real object.)

You never replied to my question, from about two months ago: What is the smallest positive Real number?

##### Full Member
Hi guys, I'm so confused about max of two points that they are the same, I mean if I have max(5,5) => 5
but I dont understand this, because max means the greatest point upon the points we have, but we have 5 ,5 so we don't have maximum point because none of two points (5,5) greater than each other, so the max() should return 0 and not 5 because the two points are not greater than each other , they are equal, so we have no greater one than the other one ... so the max should return 0 ..but sounds it's wrong as the video I watched for learning .. so anyone can help how can I define the max function?

thanks alot guys!!

#### lev888

##### Full Member
You and your spouse go shopping for a bed. The salesman asks what size bed you need. You answer "Obviously, the maximum of our heights". He says "Ok, you are both 5' 8", here are our 0 size beds".

#### JeffM

##### Elite Member
The max function on a set of numbers returns the lowest number that is NOT exceeded by any number in the set. It is a greater than or equal relationship.

The min function on a set of numbers returns the highest number that does NOT exceed any number in the set. It is less than or equal relationship.

As usual, your confusion arises because you do not pay careful attention to what things mean.

#### pka

##### Elite Member
Hi guys, I'm so confused about max of two points that they are the same,
I mean if I have max(5,5) => 5 but I dont understand this, because max means the greatest point upon the points we have
You always like a formula. Well the max & min functions are well defined.
$$\displaystyle \large{\max\{a,b\}=\dfrac{|a+b|+|a-b|}{2}~\&~\min\{a,b\}=\dfrac{|a+b|-|a-b|}{2}}$$
Here are some to practice on:
$$\displaystyle \max\{1,-2\}=~?$$
$$\displaystyle \min\{1,-2\}=~?$$
$$\displaystyle \max\{5,5\}=~?$$
$$\displaystyle \min\{5,5\}=~?$$
$$\displaystyle \min\{-5,-5\}=~?$$
$$\displaystyle \max\{3,-3\}=~?$$
$$\displaystyle \min\{3,-3\}=~?$$

#### Dr.Peterson

##### Elite Member

In English, the word "largest" can be taken to suggest there are more than one (in fact, maybe more than two) different values. But in math, we define it very simply, as the member of the set that is no less than any member of the set. This applies to any size set, and does not depend on the values being different.

In any language community (such as math), you just accept the definition that people use. This is part of being human. It is pathological to do otherwise.

#### Ryan\$

##### Full Member
Hi guys! Yes it maybe easy for others but it's really hard me and I need to grasp the concept so please burden me !

if I have : 5---------------6-------------7 which "---------" is straight line , if I want the distance between 5 and 6 then I do 6-5 =1 but now if I want the distance between 6 and 7 then I do 7-6-epsilon because we already calculated the point of 6 in the distance between 6-5 .. but in math is telling me that distance between 7 and 6 is 7-6 without epsilon .. I mean without - epsilon, what's going on exactly? why we are considering the point 6 twice in distance between 5-6 and between 6-7 ? it really makes it hard for me ..I need to grasp the concept ..how the theoretical concepts define the idea of " point "?! thanks alot !
I claim if we calculated the point of 6 in distance 6-5 because we calculated the amount of distance between 6-5 , then we must wipe the point of 6 off in calculating the distance between 6-7 ! and that's because we already calculated the point of 6 in distance between 5-6 .. but apparently I'm wrong .. I don't know why any help?! maybe I define a point in a wrong way?! how math define point ?

#### tkhunny

##### Moderator
Staff member
Subtraction works. There is no epsilon.

"Point" is axiomatic. No definition needed. No need to grasp at it.

7-6 has nothing to do with 6-5.