r/learnmath

13h ago

u/cyderyt

I dont get why the epsilon delta definition works

I dont get it, for ex:

prove lim (x→1) (2x + 1) = 3

|(2x + 1) − 3| < ε

⟺ |2x − 2| < ε

⟺ 2|x − 1| < ε

⟺ |x − 1| < ε/2

Okay but why does ε / 2 only fit for delta, I dont get why its only e / 2.

(sorry if the question was worded horribly, I dont understand the topic enough to ask it well)

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tbdabbholm

13h ago

What do you mean why "it's only ε/2"? There are lots of things delta could be, it just has to be less than ε/2

cyderyt

13h ago

Sorry, worded it wrong, thank you for replying,

a better way to ask is "Why does it work so that it HAS to be less than ε/2?"

shellexyz

13h ago

You included every step required to justify why delta has to be less than epsilon/2.

tbdabbholm

13h ago

That's just how the math shakes out.…