Recent content by Natron

while it has been extensively proven that any 2D map can be colored with at most 4 colors, has any hypothesized why that is (outside the computer programmed brute force method)?

my post was mainly based on a discrete minimal scale in which length, time, mass, and energy were based upon. if such a thing were to be considered, such as a minimal energy transfer on which every other transference of energy were a multiple of then we would have to reconsider a classical...

absolutely, all those things are true, which would, if this thinking were to progress, would also have such series as 1+1+1-1+1+1+1-1... equaling zero, too. but in the Grandi's series the natural density tends towards 1/2 of either element. plus should a working solution of the Grandi's series...

and i did make a mistake in my very first posting : "#1 - each additive element of the equation is based off of integers, and divided quite neatly. if n is an even number then that element of the series is +1, if n is a negative number then that number is -1 so it should conclude that -"...

i guess what i was trying to do was infuse a bit of set theory into the problem. and in set theory the amount of even integers are equal to the amount of odd integers and you can prove this pretty simply with a couple of equations and demonstrating the one to one corresponding elements in them...

i understand the cesaro summation, but that's a technique used in convergent series, i was trying to give a reasonable explanation as to why the series equaled zero through noncontroversial methods. my thought process here was to give a very strong argument to the summation being zero. while...

I've looked over this peculiar problem and the many different forums that have tried to resolve it yet I'm confused as to why the answer simply isn't zero. for those not familiar with this problem, it is this Ʃ of (-1)^n as n goes from 0=∞ which...

it would seem that if a is irrational and b= (a rational number) - a , then this would be a perfect example of your equation coming out rational with a+b as the numerator. for example a = pi and b = (6-pi). add them together and you get 6 even though both numbers are irrational.

i don't mean to be extremely simple here, but if Planck's constant is considered to discretely divide spacetime, then wouldn't there be a conundrum with gravitational forces over extreme distances? the obscure thing that comes to mind is imagine a complete vacuum of a universe that has 2 grains...