mNo edit summary |
mNo edit summary |
||
Line 20: | Line 20: | ||
However, this is not true. |
However, this is not true. |
||
− | :<math>e = \lim_{n |
+ | :<math>e = \lim_{n → \infty} (1 + \frac{1}{n})^{n}</math> |
Thus, ''e''<sup>''ni''</sup> ≠ 0. This implies that there is a way to get a product of 0 from two nonzero numbers. This is impossible. |
Thus, ''e''<sup>''ni''</sup> ≠ 0. This implies that there is a way to get a product of 0 from two nonzero numbers. This is impossible. |
Revision as of 01:23, 31 August 2018
The theta function, as described by Gilbert Martinez on 29 Aug 2018, allows one to rotate a complex number by any angle. The nomenclature was chosen because mathematicians often use the Greek letter θ (theta) to denote angles. It's for a similar reason that the capital theta is used as the function's symbol.
As can be seen above, the theta function inputs two variables (n representing the angle of rotation and m representing the complex number to be rotated).
Theta Function Theorem
- Further reading: Gil's Theorems
The same day he created this function, he proved what he called the theta function theorem. This theorem regards when Θ(n, m) equals 0.
Martinez proved this as follows:
Assume Θ(n, m) equals 0 and m ≠ 0. This would mean the following:
Since m is nonzero, that would mean eni = 0, since multiples of 0 must equal 0. Therefore, there must be a way to exponentiate any number to reach 0. However, this is not possible unless the exponentiated number is 0. Thus, e must be equal to 0.
However, this is not true.
- Failed to parse (syntax error): {\displaystyle e = \lim_{n → \infty} (1 + \frac{1}{n})^{n}}
Thus, eni ≠ 0. This implies that there is a way to get a product of 0 from two nonzero numbers. This is impossible.