Sorry, a really noobie question but I better ask now instead of later.
I know $\displaystyle \left( \right)$ are grouping symbols, but what are $\displaystyle \left| \right|$ symbols.
It means absolute value. Basically, if the number is positive or equals zero, then putting it between | and | does not change its value, whereas if the number if negative, the sign is removed :
$\displaystyle |3| = 3$
$\displaystyle |7| = 7$
$\displaystyle |0| = 0$
$\displaystyle |-2| = 2$
$\displaystyle |-271| = 271$
Careful when analyzing functions using these symbols with an $\displaystyle x$ term in it : you need to consider two different functions : when the expression between the symbol is negative or positive.
There are some different meanings for ||
One is cardinality of a set, so if A = {1,2,4,9,11}, then |A| = 5 because there are 5 elements in A.
One is absolute value, which gives the distance from a real number to 0, so |5| = |-5| = 5.
There are some other uses too. See here and search on the page for "absolute" to find the row entry.
One likes being thanked after spending minutes looking up how to write the absolute value symbol on the keyboard, drafting the reply, giving examples and some advice, and finally replying. At least say something if the answer doesn't suit you. It really doesn't encourage further help.
Never mind.
I used to be active on Yahoo! Answers a long time ago, and it always annoyed me when people gave my posts a "thumbs down" even though my post was correct/valuable/some such. At least there's no thumbs down button on this forum...
It somewhat reminds me of a professor I had who used the term "math(s) by democracy" or "proof by democracy" whereby the solution to a certain problem was decided by vote through show of hands. If the majority voted that a statement is true, isn't that proof enough to make it a theorem?