Two or three days ago I learned something about large numbers.
I will talk about numbers small, large and extremely huge numbers.
First of all, small numbers are those which we use in normal live. Every day you use them in your math class or if you want to calculate how much money you spent.
For those numbers you dont need any special way to write them they are quite easy.
One Ten Thousand Million Billion Trillion Quadrillion
That is why in which some states write numbers, it is called short scale because in czech we have:
One Ten Thousand Million Milliard Billion Billiard…. (thats translated)
That is called long scale because there are those “illiards”
Here you can find list of numbers and their names.
Large numbers start to create some problems. If you clicked on the link I posted you probably found that after quintillions you are lost and you dont know how the hell you should remember that.
There is system to write numbers like Unvigintillion. That is ten and sixty six zeros. You probably know this because it is used pretty often: 10^66. I wont explain this for people who dont undestand it because it would be even more boring post than it is now.
At one point this is too small and even if you start to create “towers” of exponents it will look like this: 10^10^10^651682138 which is pretty nasty.
(Btw. e+x means that there is some number of numbers after that number, for example: 153,20e+2 = 153,20
25e+16 = 250 000 000 000 000 000)
So what people created are called Knuth´s up-arrows and they look like this: ↑ (alt+24).
So I will do few examples so you know how it works:
2↑2 = 2^2 = 4
4↑3 = 4^3 = 64
5↑2 = 5^2 = 25
Now you dont get it yet but it gets awesome when i add up one arrow: ↑↑
(I will just remind you that when you have more exponents on more exponents you have to go from right)
2↑↑2 = 2^2
^2 = 16
4↑↑3 = 4↑4^4^4 = 4↑256 = 1.34e+154
5↑↑2 = 5^5
^5 = 2.9802322e+17
So it means that second number tells us how many times first number will be there
It gets totally crazy with third arrow: ↑↑↑
2↑↑↑2 = 2↑↑2^2 = 2↑↑4 = 2↑2^2^2^2 = 2↑65536 = 2^2^2^2^2^2^2…. 65536 times
4↑↑↑3 = 4↑↑4^4^4 = 4↑↑1.34e+154 = well I hope you get that idea because now it gets like so crazy that I wont continue but if you want to see some other examples go here: http://en.wikipedia.org/wiki/Knuth%27s_up-arrow_notation
Well thats about all hope you get it, if not then ask me below