What is the Definition of Dimension in Mathematics?

In summary, a dimension is a measurable extent of a particular quantity, such as length, width, height, time, or space. In physics, there are typically three dimensions of space and one dimension of time, but there are theories that suggest there could be more than three spatial dimensions. Dimensions are often described as perpendicular or orthogonal to each other, allowing for unique measurement without overlap. While it is difficult for humans to visualize more than three dimensions, mathematicians and scientists use mathematical models and theories to study higher dimensions. The fourth dimension is often referred to as time, but some theories suggest there could be additional spatial dimensions beyond the three we are familiar with.
  • #1
Dimitri655
11
0
Hey guys!

After watching another awesome video of minutephysics:


I couldn't help but wonder, what is a dimension?

Thanks for your replies in advance,
 
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  • #2
I think dimension is most clearly defined mathematically, if a space need at least N numbers in anyone of its coordinate systems, then the space is of N dimension. The space-time we live in is 4 dimensional, which includes 3 number to denote location, and one number to denote time.
 
  • #3
There are many different types of definitions of dimension in Mathematics: Hausdorff, Lebesgue covering, etc.
 

Related to What is the Definition of Dimension in Mathematics?

1. What is the definition of a dimension?

A dimension is a measurable extent of a particular quantity, such as length, width, height, time, or space.

2. How many dimensions are there?

In physics, there are typically three dimensions of space (length, width, and height) and one dimension of time. However, there are theories that suggest there could be more than three spatial dimensions.

3. How do dimensions relate to each other?

Dimensions are often described as perpendicular or orthogonal to each other, meaning they are at right angles. This allows for the unique measurement of each dimension without overlap.

4. Can we visualize more than three dimensions?

It is difficult for humans to visualize more than three dimensions, as our brains are limited to processing information in three dimensions. However, mathematicians and scientists use mathematical models and theories to understand and study higher dimensions.

5. What is the fourth dimension?

The fourth dimension is often referred to as time, as it is necessary for understanding and measuring change and movement in the universe. However, some theories suggest that there could be additional spatial dimensions beyond the three we are familiar with.

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