November 2, 2024
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R3 – Addition

In R3, addition in the Wave Number system is straightforward. Opposite Values with Opposite Signs cancel each other out through interference. See the examples below:

Examples of R3 Addition

  • 1^ + 0 = 1^; i^ + 0 = i^;   j^ + 0 = j^
  • 1^ + i^ + j^ =  1^ + i^ + j^
  • 1v + 0 = 1v; iv + 0 = iv;   jv + 0 = jv           
  • 1^ + 1v  = 0; i^ + iv = 0;  j^ + jv = 0            
  • 1v + 1^  = 0;  iv + i^  = 0;  jv + j^  = 0 
    • Addition is commutative

  • 1v + iv + jv = 1v + iv + jv
  • 0 + 0 = 0           
    • Note 0 is neither ^ or v

  • 4^ + 6^  = 10^; 4i^ + 6i^ = 10i^;  4j^ + 6j^ = 10j^
  • 4^ + 6^+ 3v = 7^; 4i^ + 6i^+ 3iv = 7i^;  4j^ + 6j^+ 3jv = 7j^
  • 4v + 6^ + 3v  = 1v; 4iv + 6i^ + 3iv  = iv;    4jv + 6j^ + 3jv  = jv
  • (4v+ 6^) + 3v = 1v; (4iv+ 6i^) + 3iv = iv;  (4jv+ 6j^) + 3jv = jv
  • 4v+ (6^ + 3v) = 1v; 4iv+ (6i^ + 3iv) = iv; 4jv+ (6j^ + 3jv) = jv  
    • Addition is associative

  • 4v + 6i^ + 3jv  = 4v + 3jv+ 6i^  = 3jv + 4v + 6i^
    • Order makes no difference

Conclusion

Try these examples of R3 addition with our online calculator.

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Previous: R2 Logs

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