# How to judge whether a relation is true or false

$$x$$ is a real number, how to judge $$x+1>x$$ is true using Wolfram.

You can use FullSimplify,
FullSimplify[x + 1 > x, x \[Element] Reals]

• You don't need FullSimplify, Simplify suffices. Also, you don't need the assumption: Simplify implicitly assumes you're dealing with reals: this is, arguably, incorrect behavior. Reduce is more rigorous: Reduce[x + 1 > x, Reals] yields True, but it needs the domain specification. – John Doty Dec 27 '18 at 13:31
• @JohnDoty - Behavior of Simplify is documented. Documentation states: "Quantities that appear algebraically in inequalities are always assumed to be real." Similarly, documentation for Reduce states: "Reduce[expr, vars] assumes by default that quantities appearing algebraically in inequalities are real, while all other quantities are complex. " With v11.3 on my Mac, Reduce[x+1 > x] and Reduce[x+1 > x, x] evaluate to Element[x, Reals] which, while more rigorous, is inconsistent with documentation. – Bob Hanlon Dec 27 '18 at 14:46