The hyperreal numbers satisfy the transfer principle, a rigorous version of Leibniz's heuristic law of continuity. The transfer principle states that true first-order statements about R are also valid in *R. For example, the commutative law of addition, x + y = y + x, holds for the hyperreals just as it does for the reals; since R is a real closed field, so is *R. Since sin ⁡ ( π n ) = 0 {\displaystyle \sin({\pi n})=0} for all integers n, one also has sin ⁡ ( π H ) = 0 {\displaystyle \sin({\pi H})=0} for all hyperintegers H. The transfer principle for ultrapowers is a consequence of Łoś' theorem of 1955.