how to illustrate the set of interval notation(-infinity,+infinity)?

Question

illustrate the interval notation(-infinity,+infinity).

Answer 1

illustrate the interval notation(-infinity,+infinity).

You use round brackets, rather than square brackets.

if x e [a,b] then a<= x <= b, but

if x e (a,b) then a < x < b

Since infinity is not a number, you cannot really say that some number is equal to infinity, only that the (value of) the number tends towards infinity.

So you cannot write down b = infinity, but b < infinity is ok.

So we use a round bracket set to represent the range from -infinity to + infinity, like so

S = (-infinity, +infinity), where x e S means -infinity < x < +infinity