What is the name of the vertical bar?

Question

I've always wanted to know what the name of the vertical bar in these examples was:

$f(x)=x^2+1\mid_{x = 4}$ (I know this means evaluate x at 4)

$\int_0^4 (x^2+1) dx = (\frac{x^3}{3}+x+c) \mid_0^4$ (and I know this means that you would then evaluate at $x=0$ and $x=4$, then subtract $F(4)-F(0)$ if finding the net signed area)

I know it seems trivial, but it's something I can't really seem to find when I go googling and the question came up in my calc class last night and no one seemed to know.

Also, for bonus internets; What is the name of the horizontal bar in $\frac{x^3}{3}$? Is that called an obelus?

Answer 1

This may be called Evaluation bar. See, in particular, here (Evaluation Bar Notation:).

Answer 2

Jeff Miller calls it "bar notation" in his Earliest Uses of Symbols of Calculus (see below). The bar denotes an evaluation functional, a concept whose importance comes to the fore when one studies duality of vector spaces (e.g. such duality plays a key role in the Umbral Calculus).

The bar notation to indicate evaluation of an antiderivative at the two limits of integration was first used by Pierre Frederic Sarrus (1798-1861) in 1823 in Gergonne’s Annales, Vol. XIV. The notation was used later by Moigno and Cauchy (Cajori vol. 2, page 250).

Below is the cited passage from Cajori

Answer 3

In my calculus book, the vertical bar is called the "evaluation symbol", and this phrase is bolded when first mentioned. It makes sense, I suppose.

Copy paste from wikipedia: Division is often shown in algebra and science by placing the dividend over the divisor with a horizontal line, also called a vinculum or fraction bar, between them.

Answer 4

In the wikipedia article for the symbol no name for this particular use of it is mentioned, just that it is read as, simply, "evaluated at". It has a number of suggested names for the symbol from different situations though:

verti-bar, vbar, stick, vertical line, vertical slash, or bar, think colon, poley or divider line