Numbers come from counting. If you can't physically count to the number than it doesn't exist. Counting is just a short hand for grouping things into a location. For example I pick apples from a tree and place them in a basket. The number of apples remains the same but I am defining my counting by only the apples in the basket. So the short hand of multiplication and exponents etc. represent the physical act of counting things one at a time but is just a short hand. If you can't actually count to a number than it doesn't exist in the physical universe. You need things to count and there are only so many atoms or particle to count and then you have to have a method of grouping the things you are counting. So it involves physics. Quantum physics, time , gravity etc. Why is this number considered to be the largest ?? You have a way of defining Grahams number but carrying out the definition is in itself impossible. This is why infinity is impossible and infinity + 1 is impossible also. When you count and attempt to count higher than anyone or anything has ever counted to before you will eventually reach a number and if you try to add 1 to this number you will fail. Something physical will prevent you from counting higher.
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