Question

Discrete.....I posted a problem and I am having a hard time understanding part c.

Answer 1

I just dont see the difference between the quantifiers that state there exist a delta for all epsilon.

Answer 2

Or the quantifiers appear to be saying the exact same things in part a and part c.

Answer 3

\(\large \forall \epsilon ~\exists \delta \) : For every \(\epsilon\), there exists a \(\delta\) ...

\(\large \exists \delta~ \forall \epsilon \) : some specific \(\delta\) exists, such that for all \(\epsilon\)...

Answer 4

both statements have different meanings for the condition :
\(\large |x-a| \lt \delta \implies |f(x)-f(a)| \lt \epsilon \)

Answer 5

i think the latter quantifier order suggests that the function is staying constant around point \(\large a\) in the interval \(\large (a-\delta , ~a+\delta )\)

Answer 6

Thanks ganeshie8!

Answer 7

I would not say specific. \(\exists !\) would be unique existence, but \(\exists\) says there is at least one, but maybe more...

Answer 8

yes, i see \(\large \exists \) referst to atleast one, not just the specific one yeah