Hypermathematics is a variant of mathematics which uses concatenation as a base function instead of addition.[1] Concatenation means gluing two numbers together, which means numbers produced by hypermathematical operations are much larger than those produced by usual operations. So in hypermathematics 2+2 is equal to 22, and 43+27 is equal to 4,327.

Multiplication

It should be noted that in hypermathematics, multiplication isn't commutative nor associative, in contrast to normal mathematics. A chain of multiplications should be solved from the left to the right. Some examples are given below:

\(3 \cdot 3 \cdot 3 = (3+3+3)\cdot 3 = 333 \cdot 3 = \underbrace{3+3+3...3+3+3}_{333} = \underbrace{333...333}_{333}\)

\(4 \cdot 3 \cdot 3 = 444\cdot 3 = \underbrace{3+3+3...3+3+3}_{444} = \underbrace{333...333}_{444}\)

\(3 \cdot 4 \cdot 3 = 3,333\cdot 3 = \underbrace{3+3+3...3+3+3}_{3,333} = \underbrace{333...333}_{3,333}\)

\(3 \cdot 3 \cdot 4 = (3+3+3)\cdot 4 = 333 \cdot 4 = \underbrace{4+4+4...4+4+4}_{333} = \underbrace{444...444}_{333}\)

\(4 \cdot 4 \cdot 4 = 4,444 \cdot 4 = \underbrace{444...444}_{4,444}\)

\(5 \cdot 5 \cdot 5 = 55,555 \cdot 5 = \underbrace{555...555}_{55,555}\)

Exponentiation

Exponentiation in hypermathematics should be solved from the top to the bottom, like in normal mathematics.

\(3^3\) = \(3 \cdot 3 \cdot 3\) = \(333 \cdot 3\) = \(\underbrace{333...333}_{333}\)

\(3^4\) = \(\underbrace{333...333}_{\underbrace{333...333}_{333}}\)

\(3^5\) = \(\underbrace{333...333}_{\underbrace{333...333}_{\underbrace{333...333}_{333}}}\)

\(3^{3^2}\) = \(3^{3\cdot3}\) = \(3^{333}\)

So exponentiation in hypermathematics exhibits tetrational growth rate.

See also

Sources

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