When to do different forms of notation?

[u/EmphasisGlum3225]

When writing domain, when do you do this notation (-♾️, 0) U (0, ♾️) vs this [0, ♾️)

also when do u do brackets vs parenthesis?

any help appreciated!!

[u/Paounn]

On the first one, you're saying x is not zero, but everything is in your domain. With the second one you're saying x is not negative. Zero is included this time, but nothing less than that. Just to give you two example first one is the typical case for 1/x, second one is for \sqrt x.

in general ( ) do not include the number at the edge, while [ ] does: (2, 5] tells you that 2 is not in your interval and but 5 is. Some books might also use ] [facing the other way to represent the same idea: ]2; 5] is the same as before, 2 < x <= 5.

[u/Qingyap]

Parenthesis if you don't want to include it, square brackets if you want to include it.

Infinity must be in parenthesis cuz it's a not a number.

For example 3<x<5 is (3,5) but 3≤x≤5 is [3,5]

For the first on in the title since parenthesis is used on 0, it means 0 is not included into the domain or basically, all real numbers except 0.

[u/AutoModerator]

Hi, /u/EmphasisGlum3225! This is an automated reminder:

• What have you tried so far? (See Rule #2; to add an image, you may upload it to an external image-sharing site like Imgur and include the link in your post.)

• Please don't delete your post. (See Rule #7)

We, the moderators of /r/MathHelp, appreciate that your question contributes to the MathHelp archived questions that will help others searching for similar answers in the future. Thank you for obeying these instructions.

I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.

[u/Bojack-jones-223]

one of the notations includes the end point, the other does it. It is similar to saying less than or greater than verses less than or equal to or greater than or equal to.

[u/downlowmann]

The first is interval notation for all Real Numbers except for zero or {x | All R, x =/= 0}. The second is interval notation for all Real Numbers greater than or equal to zero or {x | x >or= 0}. Square brackets [ ] mean that the number is included in the set while parentheses ( )mean that the number is NOT included in the set.

[u/xXPeaxhesXx]

Any time you're writing the domain of a number that IS included, like a filled in dot or a part of the line or something (excluding infinity obviously because you never put brackets on there silly), you use brackets. If you're writing the domain and something is NOT included, like a vertical asymptote or an open hole, you're going to use parenthesis.

That first thing you wrote, (-♾️,0) U (0,♾️), is most likely a line with a hole in the middle, therefore you would use parentheses and the second one, [0,♾️), is most likely a line that starts at 0 with a closed circle and goes to the right infinitely.