Random
Source Code
Random
A complete inner product space. Since every inner product defines a norm, a Hilbert space is necessarily a Banach space.
Up to equivalence of norms, there's only one distinct n-dimensional Hilbert space for each n, namely R^n.
The space of all continuous real-valued functions on the closed interval from 0 to 1, with the inner product given by the integral of pointwise absolute-value products, is an infinite-dimensional Hilbert space.
7👍 2👎
ASCII 91 and 93 (and hence U+005B and U+005D). Used in matching pairs to denote stage directions in a play or additions to a quotation. In programming languages with C-like syntax, square brackets typically enclose array subscripts. In mathematics, their most frequent use is to denote closed intervals of real numbers. On Urban Dictionary, because they're used for markup and there are no escape sequences, opening square brackets can never appear in the text of a definition.
The standard QWERTY keyboard makes square brackets easier to type than parentheses, which is pretty silly considering how much more common parentheses are.
4👍 2👎
Online stores typically have customers construct before they pay a list of all the items they want to buy. This list is called a shopping cart, in analogy to real-life supermarket shopping carts, so the command to add an item to the list is typically "add to cart".
By extension, the phrase can be used to mean "I want it".
Once I found the right brand, I clicked "add to cart".
And they have a machine that can make whatever food they want out of thin air. Add to cart!
47👍 25👎
Online stores typically have customers construct before they pay a list of all the items they want to buy. This list is called a shopping cart, in analogy to real-life supermarket shopping carts, so the command to add an item to the list is typically "add to cart".
By extension, the phrase can be used to mean "I want it".
Once I found the right brand, I clicked "add to cart".
And they have a machine that can make whatever food they want out of thin air. Add to cart!
7👍 15👎
In mathematical analysis, a metric space M is complete provided every Cauchy sequence of points in M converges to a point in M.
R^n, the set of n-tuples of real numbers, and l_2, the set of square-summable sequences, are complete.
Q, the set of all rational numbers, is not complete. For example, the sequence
3, 3.1, 3.14, 3.141, 3.1415, 3.14159...
where each term is a further approximation to pi, is Cauchy in Q but does not converge to a rational number.
50👍 19👎
An acknowledgment of a spoiler very much like a spoiler alert except that it's provided after rather than before the spoiler in question. See, for example, the Dinosaur Comics strip for April 15, 2011.
By extension, any would-be warning preceded by the thing it's supposed to warn against.
"So then Snape kills Dumbledore. That's a particularly infamous spoiler." "Nice postfix spoiler alert, you numskull." / A week after the drop deadline, the registrar told me I was taking the wrong classes and wouldn't be able to graduate till next semester. Talk about a postfix spoiler alert! Does he think I'm Merlin or something?