What is the Definition of Dimension in Mathematics?

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SUMMARY

A dimension in mathematics is defined as the minimum number of coordinates required to specify a point within a space. The discussion highlights that our universe operates in four dimensions, incorporating three spatial dimensions and one temporal dimension. Various mathematical definitions of dimension are acknowledged, including Hausdorff and Lebesgue covering dimensions, which provide different perspectives on the concept of dimensionality.

PREREQUISITES
  • Understanding of coordinate systems
  • Familiarity with basic mathematical concepts of space
  • Knowledge of Hausdorff dimension
  • Awareness of Lebesgue covering dimension
NEXT STEPS
  • Research the properties of Hausdorff dimension
  • Explore Lebesgue covering dimension in detail
  • Study the implications of dimensions in physics, particularly in space-time
  • Examine the applications of dimensional analysis in various mathematical fields
USEFUL FOR

Mathematicians, physics students, educators, and anyone interested in the foundational concepts of dimensions in mathematics and their applications in theoretical physics.

Dimitri655
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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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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.
 
There are many different types of definitions of dimension in Mathematics: Hausdorff, Lebesgue covering, etc.
 

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