Power set Cardinality

Did you guys know there isn't a surjection from a set to its Power set. ZING.

x = 1

 LHS  2^1 = 2
 RHS  1 = 1
 2 > 1

assume true for x = k > 1
x = x + 1

 LHS  2^(x+1) = 2(2^x)
 RHS  x + 1
 2^x > x
 2(2^x) > 2x
 2^(x+1) > x + x
 2^(x+1) > x + 1  since x > 1

INDUCED