Is My Understanding of Domain Notation Correct?

[aleferesco]

I just have a question which I'm confused about,

this is the same right?

Domain is (-∞,0) U (0,+∞)

and

Domain D: {XER, x ≠ 0}



and this is the same right?

Domain is (-∞,0) U (5,+∞)

and

Domain D: {XER, x ≠ 0, x≠ 5}



Attempt :

I know that U is used to connect functions,

I'm asking this here since I couldn't find notation online

 

[Dick]

U means union. You are right on the first one. Not so good for the second one. D is the set of xER, where x is not an element of [0,5], the closed interval between 0 and 5.

 

[aleferesco]

(-∞,0) u [0,5] u (5,+∞) ?

do I always have to include for example the [0,5] when function is XER?

thanks

 

[Dick]

That's all of the reals. The set you are describing in the second part is the set of all real x (xER) SUCH THAT x<0 OR x>5. It has two pieces. The xER doesn't say you are including all reals, it just says you are considering ONLY reals.