Numerical methods would suffer as the exactitude of integer arithmetic would be lost, and the margin of error would only be magnified by iteration, but 'lazy' symbolic manipulation using irrational or transcendental bases could lead to the infinite length numbers cancelling out in the process, leading to surprising and interesting results. Eulers famous equation hints at such a possibility:
ei.Pi -1 = 0
Where e and Pi are both transcendental numbers, and i is the square root of -1. Essentially, Euler was like a magician who put some of the weirdest entities in the mathematical universe into a hat - and pulled out the simple integer 0.
Numerical methods would suffer as the exactitude of integer arithmetic would be lost, and the margin of error would only be magnified by iteration, but 'lazy' symbolic manipulation using irrational or transcendental bases could lead to the infinite length numbers cancelling out in the process, leading to surprising and interesting results. Eulers famous equation hints at such a possibility:
>e^i.Pi -1 = 0
Where e and Pi are both transcendental numbers, and i is the square root of -1. Essentially, Euler was like a magician who put some of the weirdest entities in the mathematical universe into a hat - and pulled out the simple integer 0.
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