Feeling stupid asking but it's been awhile ... {{{2}}} ...what is this really saying ....are the outer brackets = null?
Cheers Michelle


Hi Michelle.

Your question depends on the level of mathematics you are studying. If, as in elementary through secondary school, you use the "curly brackets" (more formally called braces), it is generally as another set of parentheses just used to group things to affect or reinforce the order of arithmetic operations. Square brackets work the same
way. So parentheses (), brackets [], braces {} all do the same thing, they just group terms together. Usually, you use parentheses on the inside and brackets and/or braces outside. It makes it easier to immediately recognize how things are grouped than just using nested parentheses. For example,

(1 + 2) / (4 - ((1 + 3) / 2 + 1)) = (1 + 2) / {4 - [(1 + 3) / 2 + 1]}

but the right hand side is easier to visually parse.

If you are working with more advanced mathematics, such as sets, then {2} means "the set containing just the element 2". A non-math metaphor for this would be: the file folder containing just one sheet of paper, and that sheet of paper has the number two written on it.

But {{2}} is not the same: it means the set containing exactly one set, which is the set containing just the element 2". Extending the metaphor, this could be: the drawer that contains just one folder in it, and that folder has just one sheet of paper in it, and that sheet of paper has the number two written on it.

So the number of braces in this case are showing you the number of enclosing containers there are.

Hope this helps,
Stephen La Rocque.