A negated relation symbol indicating "not greater than" in inequalities and order theory.
Examples
Basic inequality statement showing a number is not greater than another
3 \ngtr 5
Comparing function values at a point
f(x_0) \ngtr g(x_0) \text{ for } x_0 = 2
Statement about sequence terms
a_{n+1} \ngtr a_n \text{ for all } n \geq N