Prime Numbers as Ortho-normal basis for all numbers

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SUMMARY

The discussion centers on the concept of using prime numbers as an orthonormal basis for representing all numbers in an infinite-dimensional space. Participants explore the idea of treating numbers as vectors and suggest that any number can be expressed as a sum of prime numbers multiplied by constants, similar to Fourier analysis. The conversation emphasizes the mathematical implications of this approach, particularly in vector operations and inner products.

PREREQUISITES
  • Understanding of prime numbers and their properties
  • Familiarity with vector spaces and orthonormal bases
  • Knowledge of Fourier analysis and harmonic representation
  • Basic concepts of inner products and vector operations
NEXT STEPS
  • Research the mathematical framework of orthonormal bases in infinite-dimensional spaces
  • Explore the application of prime numbers in number theory and vector representation
  • Study Fourier analysis techniques and their relation to prime number representation
  • Investigate vector operations and inner product definitions in advanced mathematics
USEFUL FOR

Mathematicians, theoretical physicists, and anyone interested in advanced number theory and vector space concepts.

Karim Habashy
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Hi,

Can we treat prime numbers as an Ortho-normal basis of "Infinite" dimensions to represent every possible number.
Treating numbers as vectors.

Thanks.
 
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What did you imagine for vector operations and inner product?
 
I get your point, i was thinking of them as mutually independent parameters that i can represent any number as ∑a*(The prime Number), where a is a constant, like in Fourier analysis with the harmonics.

Thanks.
 

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