Question

( ) vs [ ] what makes them different??

Answer 1

[ ] Are usually on the outside of an expression, while parenthesis are on the inside.
For example, [3+(-5+2)+5]

Answer 2

Mostly, nothing. Sometimes, one is used to mark endpoints and the other not. Generally, though, a grouping symbol is a grouping symbol and no one cares.

I cannot disagree with sylvias. Most of the time, folks naturally use () first. When that gets boring, most switch to []. When that becomes confusing, many switch to {}.

Depends on what you are doing and how much you care. Many programming languages have ONLY () for grouping. Sometimes, you don't get to choose.

Answer 3

my guess is this has to do with interval notation
\[a<x<b\] is written as (a,b)
whereas
\[a\leq x\leq b\] is written [a,b]

Answer 4

just a guess of course