Here are some more examples of my Hyper Notation a notation that uses the concept of the Hyper operators to make some pretty big numbers. 5[5]5=5↑↑↑5 this is a very small number in the grand scheme of things,but if we used this type of thinking then surely all numbers no matter how large they may appear are actually just specks of dust compared to the infinite. Anyway moving onto some larger numbers of which I have not given definite names yet as I have not developed an appropriate naming system,using the example of 5[5]5 we can use this to develop an even larger number. 5[5[5]5]5 this is 5 followed by (5↑↑↑5)-2 up arrows then 5. Again who can determine what is considered a large number or not because all numbers are small in comparison to whats beyond them. An even larger number is 6[6[6[6]6]6]6 to work out how big this number is you must first stat from the inside and work out. Before we move on we must make clear of what I mean by all numbers being like grains of sand. Consider a number x and say that this is the largest number of all number,well whats stopping you from adding 1 to it to make x+1. Although adding 1 to a number does almost nothing in a philosophical sense it is very important when comparing the infinite to the finite. Now moving back to the examples of Hyper notation of which this blog is referring to,consider the following number 2[0]2=2+1+1=2+2=4. 4 as a number does not appear to be large at all and that judgement would be correct in the sense of being a finite value but 4 is in fact infinitely larger than 3. Another example that is less microscopic but equally small is 4[4]4=4↑↑4 a tower of 4 4's,this number is in fact no closer to infinity than 1 because of what I like to call the n+1 rule. The n+1 rule is a loose term I came up with that refers to the fact that no matter how large a number you can think of or come up with their will always be a number larger than it. I call it the n+1 rule because it is a solid fact that can't be disputed proving that ultrafinitism makes 0 sense. Continuing on we are now going to look at a number that may seem huge but is actually tiny or as the jolly old Romans like to call it sehr klein. Jolly old Romans of course refers to the Germans as Jolly means happy referring to the German passion of entertainment and old Romans refer to the Holy Roman Empire. 300[300]300 or 300 followed by 298 up arrows then 300 this is a number so small that it only requires 900 digits to write out in hyper notation. Before we end this discussion of the smallness of the finite we need to make one thing clear that might contradict everything have said. There is point in the natural number line when Numbers become so large that there is no way of producing them using any function in a reasonable amount of time.