User:Druseltal2005/sandbox

$$a$$ and yielding the number after $$a$$, as the 0th):
 * 1) Addition
 * $$a + n = a\!\underbrace{''{}^{\cdots}{}'}_n$$
 * The initial element a is increased by (basis) 1 n times.
 * 1) Multiplication
 * $$a \times n = 0\underbrace{(+a) (+a) \cdots (+a)}_n$$
 * The "additive neutral-element"(0) is increased by (basis) a n times.
 * 1) Exponentiation
 * $$a^n = 1\underbrace{(\times a) (\times a) \cdots (\times a)}_n$$
 * The "multiplicative neutral-element"(1) is multiplied by (basis) a n times.
 * 1) Tetration
 * $${^{n}a} = \underbrace{a^{\cdot^{\cdot^{a^{a^{1}}}}}}_n $$
 * The "exponential neutral/null-element"(1) is exponentiated by basis a n times.