>>12599051Square bracket notation works as follows:
a[1]b= a+b
a[2]b= a×b, or a added to itself b-1 times
a[3]b= a^b, or a multiplied by itself b-1 times
a[4]b= a tetrated to b, or a exponentiated by itself b-1 times
a[5]b= a pentated to b, or a tetrated by itself b-1 times
This carries on indefinitely. Let's consider the case where a,b=3.
3[1]3=6
3[2]3=9
3[3]3=27
3[4]3=7,625,597,484,987
3[5]3= Too large to write in full, equal to 3 tetrated to 7,625,597,484,987, which is a tower of exponents of the form with 7,625,597,484,987 instances of the number 3 written down.
3[6]3= Too large to write in full, equal to 3 pentated to (3 tetrated to 7,625,597,484,987).
What's interesting about this notation is that you can nest the square brackets, solving the inner ones first. For example, 3[3[1]3]3=3[6]3.
Right then, are you ready to consider Graham's number? Keep in mind that Graham's number doesn't have special significance, it's just the upper bound on an as-yet unsolved problem.
Define as 3[6]3 and as 3[]3.
Graham's number is , which is 3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[3[6]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3]3.
