Okay, so this is related to Grandi´s series. That is a problem from maths, which was first published by italian mathematician Grandi in year 1703. The problem is like this: 1-1+1-1+1-1+1-1+1... to infinity equals what? First solution would be like this: (1-1)+(1-1)+(1-1)+(1-1)+(1-1)... =0+0+0+0+0+0+0...=0. So it is zero. BUT, there is another solution: 1+(-1+1)+(-1+1)+(-1+1)+(-1+1)...=1+0+0+0+0+0+0+0+0...=1. So it is one. Now how to get out of this? BUT, to get even more complicated, there is a weirder solution. Let´s mark the sum S. Now S=1-1+1-1+1-1+1... And 1-S=1-(1-1+1-1+1-1+1-1+1...). The minus before the bracket means you have to turn every minus into plus and every plus to minus. So, we get 1-S= 1-1+1-1+1-1+1-1... But hey, that is same as S! So, we have 1-S=S. That is a simple equation with solution 1/2(or, if you want, 0,5). So 1-1+1-1+1-1...=1/2! Now, we have three possible solutions:0,1,or 1/2! Most matematicians actually think 1/2 is best solution, for some to me unknown reason. So there is just one thing we have to care about, and that is this program. It is set to count the series. The number on top is momental value. The problem is like this:the background changes color. If momental value is 1, it is black. If it is 0, it is white. And the series is counted faster aand faster. After first 5 seconds, it counts first 1. After half of the 5 seconds, 2 and half a second, it counts another 1. After half of 2 and half a second, so a bit more than 1 second, it counts another 1. So, it always halves the time. So, after 10 seconds, it will count all the 1´s. Now if the result of Grandi´s series is 1, at end it will be black. If it is 0, it will be white. If result is 1/2... What the heck? Half black half white? Or gray? But you can check there is no such background! That is the problem with this series. Obviusly, it cannot count infinity 1´s in finite time, because counting another part takes some time, so the program will only switch between black and white quickly, but you get the point.And by the way, if you read all the way here, congratulations! I hope you will write something in comments as I really want to start a discussion. Give a like or favourite and thanks for reading!
Some mathematical stuff, but if you are anyhow interested, read above! Warning for epileptics!
