what is the math definition of negative
A negative number is a number $x$ such that $x+y=0$ for some positive number $y$. In other words, a negative number is an object whose sum with some positive number equals the additive identity. A similar approach can be used to define other mathematical objects: $ 1 x=0$ is an object such that $a+x=a$. $ 2 x=\frac{1}{a}$ is an object such that $xa=1$.