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If BEAF is the most well-known of the less-known large number notations, then in second place probably falls Sbiis Saibian's Extensible-E (ExE) System. It's a large number notation much to the likes of BEAF, divided into subsystems each more advanced than the previous, and with a vast amount of googolisms to its name. Just like we've spent the past few articles learning about Bowers' linear array notation (the first subsystem of BEAF), today we'll learn about Hyper-E notation (E#), the first subsystem of ExE. And just as we spent a good deal of time looking at the backstory of Bowers' legendary notation, we'll go into heavy detail on the origin of Saibian's system, which started as the adventures of an imaginative little second-grader.
sites.google.com)Although he didn't know it at the time, his friend's father was probably incorrectly explaining the googolplex. Somehow the man managed to mess up the name of the number, the definition, AND the origin story - that's three botch-ups in one! There never was such a number as a googolgong, only the ever-famous googol and googolplex, which are 1 followed by 100 zeros and 1 followed by a googol zeroes respectively. And it's pretty funny to imagine that "scientists" would be the ones to come up with such a large number for the sake of it - that's just not something that people who study science would do. Instead, a single mathematician and his nephew came up with the googol and googolplex, not a team of mad scientists researching whatever. (Source:
Now that's a really powerful notation - powerful enough that you can't directly relate it back to even stack notation, which is the largest notation in Saibian's system that can be easily understood in terms of standard math notation. In terms of hyper-operators it's on par with hexation. You can express a hexated to b in 5-cell notation by making the base equal to a, the third replicator b, and all other cells 1.
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