Question

please explain this about intervals what is - infinity and+infinity

Answer 1

let any number P less 10 ,
then you how to write this
P< 10
it is correct !! because we know, number is less then 10 but we don't know lower limit of P so, we assume it limit less then -∞
e.g P< 10 we also write this ,
-∞ < P < 10

now, if any number Q greater then 20
we can write this Q> 20
due to we don't know about upper limit of Q , so, we assume upper limit of Q less then ∞
hence, we can write 20 < Q <∞

now, let any number E is belongs to all real number ,
then we how to write this ? ???
actually we don't know, minimum and maximum number of E so,
we can E is less then ∞ and greater then -∞
e.g -∞ < E < ∞ , E €( -∞ , ∞)

Note :- we can't say any number is equal to ∞
example :-
P€ [ -∞ , ∞] this is wrong , because this is not a set of well defined. and no any number we can write .
so, P €( -∞ , ∞) is correct . this is defined and possible .