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

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You can use FullSimplify,

FullSimplify[x + 1 > x, x \[Element] Reals]

True

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    $\begingroup$ 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. $\endgroup$
    – John Doty
    Dec 27, 2018 at 13:31
  • $\begingroup$ @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. $\endgroup$
    – Bob Hanlon
    Dec 27, 2018 at 14:46

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