Question

Formal Definition of Limit. I will provide a jpg image containing the problem i'm having...

Answer 1

1) you see x=a, and a does not belong to union of these open sets (x1,a) U (a, x2), since a is in neither of them

Answer 2

\[(a - \delta, a ) \cup ( a, a + \delta ) = 0 < | x - a | < \delta\]

Answer 3

plz explain why this equality

Answer 4

(a−δ,a)∪(a,a+δ) - > 0<|x−a|<δ i couldn't understand this

Answer 5

2) \( \delta \) is the length of interval a - x1 and x2 - a <= so it can equivalently said

Answer 6

3) is combinatio of 1 and 2

Answer 7

x1 = a−δ
x2 = a+δ

Answer 8

combinatio ? 1st i have heard of it ...

Answer 9

they both are definition of limit
1) in terms of metric space
2) in terms of set.

Answer 10

i hve got :) thanks alot.. :) really thnks :) Experiment... :)

Answer 11

forgot X at the end ... lol
you are welcome.

Answer 12

yah.... :) i noted :)

Answer 13

i hd understood :)