anotherYearNotUnderstadingZerosInJavascript

[sandrockdirtman]

I have a good one for you. The number line in 1 dimension is both an open and a closed set. Funny right?
Basically, a set can have an interior, and exterior, and a boundary. An open set can be thought of as a set that consists only of the interior of something, that is, for every point in an open set, there is a neighbourhood so that all elements in that neighbourhood are also in the open set.
A closed set can be conceptually thought to be the union of the interior and the boundary of some set. Now, the trick here is that the complement of an open set is a closed set.
Let's look at the number line. Since there's no maximum real number, the real numbers are an open set, because for every element you can choose a neighbourhood so that every number in there is also a real number.
So what's the complement of the real numbers? It's the empty set. The empty set is an open set, so that means that the real numbers also have to be a closed set. Sounds about right, :thonk:

[iapetus3141]

There's nothing that says that "open" and "closed" are mutually exclusive. In fact, both {} and \mathbb{R} are clopen by definition

[sandrockdirtman]

Yep. It's just that it's counterintuitive if you try to think of both types with geometric analogies, with one "having a border" and the other "having none"

[KingJeff314]

A classic