How Can I Prove Continuity Using Epsilon Delta Definition?

[Fisicks]

Recently in adv calc we have been dealing with the epsilon delta definition for continuity, and my professor said that it is ok to assume that delta<1. I actually used this to show that x^4 satisfies the epsilon delta condition but I'm not quite sure why we can take delta<1. I am sure you guys know the definition and it doesn't restrict delta at all.

I'm hoping someone can refer me to a resource or just give me some kind of insight.

Thanks

 

[disregardthat]

Well, it rests on the simple fact that if |x-y|<min(delta,1), then |x-y|<delta.

 

[Skrew]

Because you only care about it in some arbitrarily small neighborhood.

You could assume delta < .1 and base a proof off it.