# Tagged Questions

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### $\Bbb Z^\ast$ What is this notation?

What does $\Bbb Z^\ast$ mean? I would think some subset of the integers but I cannot find a definition. Thank you.
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### Set-builder defining set size and valid elements? Notation help.

I'm working on some documentation for a system that uses an arbitrary waveform generator that accepts data with a number of requirements. I would like to include some formal definitions of the ...
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### Cannot understand a mapping function which include some sets

I have kept a screenshot of my problem below which describes about the various sets. At the last line, there is an expression where a function delta uses those sets and maps them into another. I am ...
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### Notation for choosing the k smallest elements from a set of integer

Is there any specific notation for picking $k$ elements from a set which are the smallest? Ex: {$1,3,5,7,9,11$} with $k = 3 \Rightarrow$ We want $1,3,5$
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### Set question - $ℤ^+ = ℕ$ [duplicate]

I am not sure whether the following statement is true: $ℤ^+ = ℕ$ if not, why? Thank you in advance! I appreciate your help!
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### How to write $A\cup\emptyset\times A\cup\emptyset$

How to write the cartesian product of this? $$(A\cup\emptyset)\times (A\cup\emptyset)$$ Is it: $$A^2\cup\emptyset^2?$$ What does $\emptyset^n$ means?
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### $\mathcal N (A):=\mathcal P(A)-\varnothing$ notation

Define $\mathcal N$ $\mathcal N (A):=\mathcal P(A)\setminus\{\varnothing\}$ Does $\mathcal N$ has a special name and standard notation?
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### Notation question in elementary set theory

Let $A$ be a set. What is defined as $UA$? Is it the union of all sets that $A$ includes? Could someone provide an example for this notation? Thank you!
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### Notation in set theory.

What is the difference between these two notations? $\{a_k\}_{k\in K}$ $\{a_k, k\in K\}$ Is this correct? $\{a_1\}$, $\{a_2\}$, $\dotsc$ $\{a_1, a_2, \dotsc\}$ Or 1. and 2. are the same? Is ...
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### Constructing sets involving predicates. Let $P(x),Q(x)$ be predicates over a set $X$?

Let $X$ be a set and $P(x),Q(x)$ be predicates over $X$. Consider the sets $$Y = \{y\in X\mid P(y)\}$$ $$Z = \{z\in X\mid Q(z)\}$$ Complete the following sentences with quantified propositional ...
Is there a correct notation to indicate multiplying all elements within a set? For example, if $M = \left\{n_0, n_1, ..., n_t\right\}$ be the set of elements where I want to multiply all the numbers ...
The identity relation on a set $A$ is $\operatorname{id}_A = \{(x;x) \,|\, x\in A\}$. This can be generalized for any (possibly infinite) index set $N$ as $\{(\lambda i\in N: x) \,|\, x\in A\}$ (here ...