User blog:IIEnDeRwITHeRII/Node Function

The Node Function n(m) is defined as the minimum time elapsed for m numbers ($$x_1, x_2,...,x_m$$) to match in nanoseconds, if each $$x_m_$$ for any m had 100000000 possible numbers.

This function is uncomputable because of its highly variable nature due to different computer's different processing speeds. As such, it is impossible to find a definite value for any m in n(m). It is only possible for upper limits to be calculated for any m in n(m).

Googology Wikia user IIEnDeRwITHeRII first coined this function in 2018, on May 11th.

He has also found some upper values of n(m) for n = 1 and n = 2.

For n(1), the result is 0, because comparing something against itself is completed instantly. n(1) is also the only node value that can be exactly calculated.

n(2) has an upper limit of 341334.

For n(3), the function is difficult to calculate in one day with my lowly computer I possess, so I am going to leave this to the community of googology.

Generally, for n(m) with m > 5, the function becomes impossible to calculate because of the time of the program running.