Basic basic set theory. Please help. Simple answer will suffice.

AI Thread Summary
The discussion revolves around a high school student, Andy, who is confused about the use of ellipses in set theory notation. Participants clarify that ellipses, represented as "...", indicate that a sequence continues, such as in the example of positive odd numbers. They explain that this notation helps avoid listing every element in a set, making it more concise. Additionally, ellipses can signify pauses in sentences or indicate omitted parts of quotations. Overall, the conversation aims to clarify the function and meaning of ellipses in mathematical contexts.
andrewkg
Messages
86
Reaction score
0
Hello my name is Andy I'm in high school, and I have a bit of a confusion or lack of information. Ok so I have been reading a book on set theory, and I keep encountering … ,but up more in the use of a set. Like A,B … but again up more to the middle of the sentence. I feel dumb, I googled it nothing, I've been thinking about it for around 2 hours. I cannot sleep it is bugging me so much. Thank you in advanced!
 
Physics news on Phys.org
I keep encountering … ,but up more in the use of a set. Like A,B … but again up more to the middle of the sentence
You mean you keep encountering three dots like this "..." or "##\cdots##"?
They are called "ellipsis" and stand for the words "and so on", and mean that things continue as implied by what went before.

So:
##A,B,\cdots## means start going A B C etc and keep going in the same pattern ... so ##\{ 1,3,5,\cdots \}## would represent the set of positive odd numbers
##\{ 1,3,5,\cdots,27,29 \}## would be all the odd numbers from 1 through to 27 inclusive.
They are written like that because it would be boring to list every single member.

In a sentence it indicates, informally, a longish pause - in a quotation, it means that part of the quote that goes there was deleted for clarity.
At the end of a sentence it indicates that the sentence has been deliberately left unfinished.

See:
http://www.mathsisfun.com/sets/sets-introduction.html
http://en.wikipedia.org/wiki/Ellipsis
 
I was reading documentation about the soundness and completeness of logic formal systems. Consider the following $$\vdash_S \phi$$ where ##S## is the proof-system making part the formal system and ##\phi## is a wff (well formed formula) of the formal language. Note the blank on left of the turnstile symbol ##\vdash_S##, as far as I can tell it actually represents the empty set. So what does it mean ? I guess it actually means ##\phi## is a theorem of the formal system, i.e. there is a...
Back
Top