Epsilon Delta

  • Thread starter Fisicks
  • Start date
  • #1
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Main Question or Discussion Point

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. Im 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
 

Answers and Replies

  • #2
disregardthat
Science Advisor
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Well, it rests on the simple fact that if |x-y|<min(delta,1), then |x-y|<delta.
 
  • #3
129
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Because you only care about it in some arbitrarily small neighborhood.

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

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