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## Main Question or Discussion Point

Hi all,

I'm trying to teach myself analysis using the book "A Companion to Analysis: A Second First and First Second Course in Analysis" by T. W. Körner.

There's an inequality problem in there that's used to prove a statement about the continuity of a function, that I've got stuck in (problem 1.16, part (iii), in case you happen to have the book):

Working in [itex]\mathbb{Q}[/itex] (the space of rational numbers), if [itex]x^2<2[/itex] and [itex]\delta=\frac{(2-x^2)}{6}[/itex], show that [itex]y^2<2[/itex] whenever [itex]|x-y| < \delta[/itex]

Any help would be greatly appreciated!

I'm trying to teach myself analysis using the book "A Companion to Analysis: A Second First and First Second Course in Analysis" by T. W. Körner.

There's an inequality problem in there that's used to prove a statement about the continuity of a function, that I've got stuck in (problem 1.16, part (iii), in case you happen to have the book):

Working in [itex]\mathbb{Q}[/itex] (the space of rational numbers), if [itex]x^2<2[/itex] and [itex]\delta=\frac{(2-x^2)}{6}[/itex], show that [itex]y^2<2[/itex] whenever [itex]|x-y| < \delta[/itex]

Any help would be greatly appreciated!