Tetration

As mentioned in the last post, 2↑↑2=4, but what does the ↑↑ symbol mean? ↑↑ is a symbol (there are many notation systems, like ^^) for the operation known as tetration. Anyone with a basic knowledge of mathematics will know that multiplication is just repeated addition, and that a*b is the same as adding a to itself b times. Exponentiation is similar, a^b is just a multiplied by itself b times. Tetration, now, is an extension of these. a↑↑b is a to the power of itself b times, so 3↑↑3=3^3^3. As you can probably tell, tetration makes big numbers quickly, and isn’t supported by many calculating devises, or at least not for very long. Here’s some tetration involving 2:

2^^1=2

2^^2=4

2^^3=16

2^^4=65536

2^^5=2^65536≈2*10^19728

And some involving 3:

3^^1=3

3^^2=27

3^^3=7625597484987

3^^4=3^7625597484987≈10^10^10^1.01

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