# Tag Info

## Hot answers tagged notation

10

The notation means : $q$ divides $k$ ; There is an integer $m$ with $qm=k$.

5

The second notation means "decreasing to", the first just "going to". In the same way you can use the "increasing to" arrow: $\nearrow$. Both "increasing to" and "decreasing to" implies "going to" but the vice versa does not hold. Sometimes $\uparrow$ and $\downarrow$ are also used.

4

It is the boundary of the ball.

3

subscript is a derivative with respect to this variable. $$u_{xx} = \frac{\partial^2u}{\partial x \partial x}$$

3

Well i can only assume what you are looking for. By the term in your question i think you might mean a superfactorial. See this Wikipedia Article on Factorials - it might help. If you mean a product of factorials it would be a notation like $$sf(n)=\prod^n_{k=1}k!$$

3

It is one of the common notations for numeral systems in different bases. In this case it is the ternary system. See, $12_3=1\cdot3^1+2\cdot3^0=5$.

2

The paper explains the notation in the footnote on page 2: It uses hollow square brackets $[\![\cdots]\!]$ as a notation for the Iverson bracket, which by definition means "$1$ if the claim inside the bracket is true; $0$ if it is false". Thus, $y=2[\![c_k=c_{\rm min}]\!]-1$ is just a terse way to write $$y = \begin{cases} 1 & \text{if }c_k=c_{\rm min} ... 2 One way to write it is: \forall i, j: 1 \le i \lt j \le n \implies A_i \cap A_j = \emptyset (Although it seems a lot easier to understand the way you stated it!) 2 It really depends on what you want to express, do you want to describe that the events are mutually intersection free, then write it as Dan Brumleve suggests as$$ \forall i, j: 1 \le i \lt j \le n \implies A_i \cap A_j = \emptyset $$if you want to express that the sets (events) are indeed mutually independent to some probability measure, then you might be ... 2 U is some other normed vector space. In this case L^2([0,T];U), sometimes lazily written as L^2(0,T;U), consists of functions f from [0,T] to U such that \int_0^T \| f(t) \|^2 dt<\infty, where \| \cdot \| is the norm on U. This notation is used in, for instance, Partial Differential Equations by Evans. Most commonly the U in question ... 2 It means that p^{\alpha}\mid n but p^{\alpha+1}\nmid n. For example. 2^2\mid 12 but 2^3\nmid 12. Hence 2^2\|12 2 This is not a mathematical term but a figure of speech. One says that A is an honest B to assert that A satisfies the definition of B. Usually the reason to emphasize honest is that A was informally called "B" earlier in the text. This is associated with a somewhat conversational style of writing. Specifically for distance functions, this word would ... 1 It means that q divides k, or k is divisible by q. Add a little slash and it negates that meaning: q \nmid k means q does not divide k. For example: 3 \mid 1728, 3 \nmid 1729. They are not relatively prime, unless q = 1 or -1. In fact, if q \mid k then \gcd(q, k) = |q|. 1 According to my Differential Geometry professor, it means that the closure of V_{\alpha} is contained in U_{\alpha}. According to Silvia Ghinassi and other sources, it generally means that the closure of V_{\alpha} is a compact subset of U_{\alpha}, in which case the notation V_{\alpha}\Subset U_{\alpha} is read "V_{\alpha} is compactly ... 1 u is a two variable function u(x,t),$$u_{xx}=\frac{\partial^2x}{\partial x^2}.

1

$x+x-2x \equiv 0$ but $x^2+1=0$ is for only $x= \pm 1$. The first represents an identity which holds for all $x$ while the other is conditional equal which may or may not have solutions.

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