# Tagged Questions

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If $\left ( X_{i} \right )_{1\leq i\leq n}$ is an ordered n-tuple of sets their Cartesian product is defined as: $$\prod_{i=1}^{n}X_{i}:=\left \{ (x_{i})_{1\leq i\leq n} :x_{i}\in (X_{i}) \; \text{ ... 1answer 44 views ### tuple of tuples notation Is the following notation right for indicating a \mathit{m}-tuple of \mathit{n_{j}}-tuples (I mean that each tuple of the \mathit{m}-tuple has a different number of elements)? ... 2answers 62 views ### Basic Cartesian prodcuts I am having some issues grasping basic ideas of Cartesian products. I am reading a PDF my professor gave us explain sets/Cartesian products. If \mathbb{R}\times \mathbb{R} can be written as ... 2answers 34 views ### How to repesent n x m multiplication into symbol notation? I am not a mathematician and so I might not be using the right terms. I have a vector of n components and another vector of m components ... 0answers 79 views ### Notation for Kronecker product of a matrix and itself? What is the notation for the Kronecker product of a matrix and itself? In other words, is there a short-hand way I can express the following: X⊗X X⊗X⊗X X⊗X⊗X⊗X Where X is a matrix? What ... 1answer 41 views ### Is it generally preferred that empty products are gotten rid of where possible? Is it generally preferred that empty products are gotten rid of where possible? For example: Stewart's structure theorem says that for a positive integer n, every positive integer \leq n has a ... 4answers 98 views ### Big Greeks and commutation Does a sum or product symbol, \Sigma or \Pi, imply an ordering? Clearly if \mathbf{x}_i is a matrix then:$$\prod_{i=0}^{n} \mathbf{x}_i$$depends on the order of the multiplication. But, ... 2answers 100 views ### Summation and Product Bounds If I have a sum or product whose upper index is less than its start index, how is this interpreted? For example:$$\sum_{k=2}^0a_k,\qquad \prod_{k=3}^1b_k$$I want to say that they are equal to the ... 0answers 92 views ### “Product” bundle notation. Let \newcommand{\Spin}{\operatorname{Spin}}M and M' be two manifolds, equipped with a principal \Spin_n and \Spin_{n'} bundle called P and P', respectively. Then there is an induced ... 4answers 259 views ### Derivative of product notation? Presume f(x,y) is a continuous function. How would I take the derivative of$$\prod_{x=1}^N f(x,y)$$? Edit: derivative with respect to x, that is. 1answer 114 views ### Limit of an n-ary product Since a definite integral is defined as$$\lim_{n\to\infty} \sum_{i=0}^n f(x_i^*)\,\Delta x = \int_a^b f(x)\,dx and the integral is much easier to calcluate than a sum, if we change the sum to a ...
$(x + x + \cdots + x)$, where $x$ added $n$ times can be written as $x * n$. $(x * x * \cdots * x)$, where $x$ multiplied $n$ times can be written as $x ^ n$. Is there an operator, such that if ...