# Who came up with a formula expressing the sign function in terms of the absolute value?

I read here and here that Karl Weierstrass used "| |" to indicate absolute value in 1841. The same sources indicate that Leopold Kronecker wrote of the sign function in 1878. Here it is indicated that the sign function may be expressed via the absolute value function, $$\textrm{sgn}(x)=\frac{x}{|x|}$$, but no history of the practice is indicated. Any leads on who put them together if it wasn't Kronecker in 1878?

• I don't really think there's any connection between the two other than that they deal with both positive and negative numbers. – Carl Witthoft Jan 3 at 14:26