# Does point really exist?a mathematical concep

• danger9
In summary, the concept of "point" in mathematics is abstract and has no physical existence. It can be used in non-mathematical ways, but in mathematics, it is a mathematical idealization. "Reality" is not a useful concept in mathematics or physics, as these fields focus on what is observed rather than what "really" causes it.
danger9
does point really exist in reality or it is mere a mathematical concep

The word "point", as used in mathematics, is a mathematical concept. That is true of any word used in mathematics. If the mathematics is a from a physical problem, then the word "point" may refer to a mathematical idealization of a real object.

Of course, the word "point" can be used in non-mathematical ways ("The first point of land we see will be ...", "is there some point to this discussion") in which the "point" may "exist in reality".

danger9 said:
does point really exist in reality or it is mere a mathematical concep

It is just a mathematical concept, like numbers. It is abstract. You may ask yourself questions like: "what is the size of a point ?" If it has no size, then it must be nothing. But in mathematics we measure sizes using measures, like The Lebesgue measure. The Lebesgue measure of a point is 0. But there's even uncountable sets with measure zero.

In reality, things are very different and more weird, because if you want to measure a very tiny tiny particle, it will not be there before you measure it. If I told you to point your pen in the real axis to indicate the position of the value 1.4, you will just give me a region with the size of the head of the pen. But when you go smaller and smaller, you suddenly enters a world where space has no sense, even time is not defined (see the delayed choice quantum eraser experiment). So even the word "reality" you used in your comment makes no sense in this scale.

Even if this approach of giving an object a place using a point doesn't work in tiny scales, Mathematics seem to always give beautiful formulations of even weird things like quantum physics.

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danger9 said:
does point really exist in reality

"Reality" doesn't exist as a mathematical concept - at least not as a concept that is well known enough to have a standardized definition. Mathematics itself doesn't answer the question about whether something exists "in reality".

Perhaps you mean "reality" in the sense that the word is used in Philosophy or Physics. The forum has rules against discussing Philosophy (I've never understood the scope of these restrictions, perhaps you can talk about it in "General Discussions") If you can formulate your question so it is concrete and specific, you might be able to get an answer in the Physics sections.

Perhaps you mean "reality" in the sense that the word is used in Philosophy or Physics.
Leave "reality" to the Philosophers. It's not a useful concept in physics either. Physics is about what is observed, not about what "really" causes what we observe.

AlephZero said:
Leave "reality" to the Philosophers. It's not a useful concept in physics either. Physics is about what is observed, not about what "really" causes what we observe.

That seems ironic considering the entire point of physics is to find mathematics and explanations that accurately conform to the evidence of "reality" based on specified parameters, which can then be applied as a general rule. Why would physicists be looking for a theory of everything if they were not interested in finding out what really causes what we observe?

Good replies everybody! It seems like a good place to end the thread.

## 1. What is a point in mathematics?

A point in mathematics is a fundamental concept used to represent a specific location or position in space. It has no length, width, or thickness, and is often represented by a dot or a cross.

## 2. How is a point different from a dot?

In mathematics, a point is an abstract concept that has no physical dimensions, whereas a dot is a physical mark that has a finite size. A point is used to represent a specific location, while a dot is often used as a symbol to mark something or as a component of a larger object.

## 3. Is a point the same as a coordinate?

No, a point and a coordinate are not the same. A point is a general concept representing a specific location, while a coordinate is a specific set of numbers used to represent the position of a point in a coordinate system.

## 4. Can a point really exist in physical space?

No, a point is an abstract concept that does not have a physical existence. It is used as a tool in mathematics to represent a specific location or position in space, but it does not have any physical properties.

## 5. How is a point used in geometry?

In geometry, a point is used as a basic building block to define other geometric objects such as lines, planes, and shapes. It is also used to represent the location of important features or intersections in a geometric figure.

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