User:AbnormallyNormal

AbnormallyNormal (talk) 12:19, 17 August 2008 (UTC)user page

2 + 2 = 2 * 2 = 2^2 = 2^^2 = 2^(N)^2

1 + 2 + 3 = 1 * 2 * 3

it is not the case that for all a, b, belonging to C, a^b = b^a, or for all a, b, c belonging to C that a^(b^c) = (a^b)^c. there does exist a, b, belonging to C such that a^b = b^a, and a, b, c, belonging to C such that a^(b^c) = (a^b)^c.

2^3 < 3^2; 2 < 3; 3^4 > 4^3; 3 < 4; 1^2 < 2^1; 1 < 2; 2^4 = 4^2; 2 < 4; 4 = 2^2, hence 2^4 = 2^(2^2) and 4^2 = (2^2)^2. special case of valid associativity and commutativity for exponentiation.

0^0 = 1. 0^x for x > 0 = 0. 0^x for x < 0 has limit to infinity. tan-1(0) = 0, tan-1(infinity) = pi/2, tan-1(1) = pi/4. horizontal, vertical, diagonal slopes.

2^^3 = 2^2^2 = 16. 3^^2 = 3^3 = 27. 2^^3 < 3^^2, 2 < 3.

if x < y, then y > x.

3^^4 = 3^(3^(3^3)) = 3^7625597484987 = ? 4^^3 = 4^(4^4) = 4^256 ~= 1.3 * 10^154. 3^^4 > 4^^3. 3 < 4.

the wrap around of exponents for 'e' continues with tetrants.

n^^1 = n^1 = n.

n^^(m + 1) = n^(n^^m).