FullSimplify with ForAll

*To*: mathgroup at smc.vnet.net*Subject*: [mg48624] FullSimplify with ForAll*From*: csr at postmark.net (Sharath)*Date*: Tue, 8 Jun 2004 00:48:15 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Given the input (Mathematica 5.0) a = (d + 2)/d; b = (1/a)^(1/r^2); FullSimplify[ForAll[{r, d}, r>=1 && 0 < d && d < 1, 1 - b^(r^2) > 0]] the output is \!\(∀ \_\({r, d}, r ≥ 1 && 0 < d && d < 1\)1 - \((\((d\/\(2 + \ d\))\)\^\(1\/r\^2\))\)\^\(r\^2\) > 0\) which is the same expression with b expanded, that is, forall{r,d},r>=1 && 0<d && d<1 1-((d/d+2)^1/(r^2))^(r^2)>0 Why is FullSimplify not cancelling 1/(r^2) and r^2? My interest is a more complex inequality but FullSimplify is just giving me the expression back. Then I tested with this simpler inequality and it still gives me the expression back. Could anyone know how I should give the input? I want to see if the expr is Ture or False. Thanks, Sharath

**Follow-Ups**:**Re: FullSimplify with ForAll***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>