Multiplication is just defined as doing addition over and over. 4*3 is the same as 4+4+4 as you are asked to add 4 to itself 3 times. Similarly, 4^3 is asking you to do 4*4*4, so multiplying 4 to itself 3 times. You can use similar logic to make a notation that makes you do 4^4 to itself 3 times. These numbers get very big, very fast. I only went to three degrees of that logic but Graham’s Number makes you do it to the 64th degree, which is absurd to the point of being incomprehensible.
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