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Hypermathematics is a variant of mathematics which uses concatenation as a base function instead of addition. 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.