What does a mathematical ''point'' look like?

Answer 1

There is one to one correspondence between the point and the number on number line. For every number, you have a single point on the number line. For every point on the number line, you have single number that exists. So between any two given points, you have at least one point. That only means that there are infinite points between any two given points. This can be proved very easily. Between 0 and 1, you have 1/2. 1/2 can be written as 1000/2000. 1 can be written as 2000/2000. So you have 1001/2000 to 1999/2000 points there. Like 1001, 1002, 1003.......1999. I can take bigger and bigger figure. I can get infinite points between any two points, like this. So if you want to travel from one point to another point, point by point, the distance is too near, yet it's too far.One great scientist presumed that the shape of the point is very tiny square. That is not correct. For every square, you have four points. Again that every single point will have four points. The process never ends.

Here comes the role of psychology. From the birth, you are trained 'to look' at every thing. You can not think about the point without looking at the same. The point does exists. As the line is made up of (infinite) points. The plane does exists. As the plane is made up of (infinite) lines. The three dimensional space does exists. As it is made up of (infinite) planes.

So in between 0 and 1 you have infinite points. Between 0 and 2, you have infinite * 2 points. Between zero and 3, you have infinite * 3 points. This way you have infinite 'sizes' in the infinite. Some are 'small infinite' and others are 'large infinite'.

This is ridiculous.

So mathematically the point is a unit that exists and does not exists also. Here you do not have one point in contact with the next point. Between any two points, there are infinite points. It is some what like wave particle duality. As Albert Einstein wrote: "It seems as though we must use sometimes the one theory and sometimes the other, while at times we may use either. We are faced with a new kind of difficulty. We have two contradictory pictures of reality; separately neither of them fully explains the phenomena of light, but together they do". Because with anything that exists, you can travel at least some distance when you collect many of them. Here between any two points there are infinite points. So if you want to travel, point by point, from one point to the other point, you may not reach there in any given number of steps.

The fact is that any number is 'same' and can be taken as 'zero' as compared to infinity.

I will like to explain this statement further. Suppose you travel step by step on number line. Say 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.......! Then suppose you take each step of say 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000......! It looks very logical that the one taking step of 100 will reach to infinity faster or earlier. Does either of the traveler reach to infinity? Infinity does not care about the length of your step. You simply do not reach there. That is why I say that infinity is a concept beyond the perception of human brain. Point is infinitesimally small. Here again infinite word has come. You can not have perception of the same. That is beyond the capacity of the human brain to understand the concept of point.

I do not know about the number of persons, who can get this concept. If nobody gets it, there will be somebody in the future generation, who will get the same.

The conclusion is that point lie between existence and non existence.

The further conclusion is that there are so many things, those are beyond your capacity to understand or capacity to process by thinking, imagination, reasoning and logic!

(The same thing I encountered, when I tried to understand Bhagwadgeeta. There is that (Infinite) God, who is trying to make the human brain understand HIM from different angles and views. The human brain of Arjuna is not getting HIM due to inherent inability to understand (Infinite) HIM. Here Lord Krishna has tried to explain Arjuna about infinite God in many different ways and means. Also here Lord Krishna has said repeatedly that unless you love others, you can not go to HIM. The same thing must be true for most of the religious books. They are more misunderstood than understood and now we are trapped in lot of trouble. Everybody is same and equal as compared to God. That is why Jesus Christ said that you love others, like you love yourself.)

Answer 2

A mathematical "point" has no dimensions. Zero length, zero width, and zero height. It is, as far as our actual senses are concerned, an imaginary construct, not truly describable in physical terms, despite its usefulness.

Answer 3

It does not, It is an idealised concept representing a position is space. It has no dimensions and hence no size and so would not be invisible to the human eye or even the most powerful microscope imaginable.

Answer 4

A mathematical point would not look like anything since it would be infinitesimally tiny. So small that you would never be able to see it.