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## Homework Statement

If a<b...can I then say that [itex]a^2<b^2[/itex] or [itex]a^3<b^3[/itex] or even [itex]\sqrt{a}<\sqrt{b}[/itex]?Why I ask is that usually in some of the induction questions I do with inequalities, they give an expression like [itex]x_{n+1}=x_n^2 -7 [/itex] or something like that.