# What is Set notation: Definition and 31 Discussions

In set theory and its applications to logic, mathematics, and computer science, set-builder notation is a mathematical notation for describing a set by enumerating its elements, or stating the properties that its members must satisfy.Defining sets by properties is also known as set comprehension, set abstraction or as defining a set's intension.

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19. ### Building a set notation part II

Homework Statement As an exercise , the book I'm reading ask me to build a set notation for the following set: ##\{... \ , \frac{1}{27} \ , \frac{1}{9} \ , \frac{1}{3} \ , 1 \ , 3 \ , 9 \ , 27 , \ ...\}## The Attempt at a Solution After playing with the numbers a couple of minutes , I came...
20. ### What is the set notation for a sequence with a common difference of 3/4?

Homework Statement The book I'm reading ask me to build a set notation for the following set: ##\{-3/2 , -3/4 , 0 , 3/4 , 3/2 , 9/4 , 3 , 15/4 \}##. The Attempt at a Solution I attempted to build a set notation and came with the result: ##\{ x \in R : \exists y\in Z \ \ y(3/4)= x\}## My...
21. ### Need help with writing set notation.

I need help with some set notation. I am an engineering major and don't know the proper notation. I am trying to write two statements. I have two sets, x_1 = {1,2,3}, and x_2 = {4,5,6}. Verbal Statements: y_1 was measured for all values of x_1 and x_2 y_2 was measured, for all values of...
22. ### Use set notation to define the language generated by the grammar

Homework Statement As the topic states, I need to define a language, for a grammar, using set notation. Homework Equations Here is the grammar: S -> aaSB | λ B -> bB | b The Attempt at a Solution Okay, I know that this creates strings that are either empty or consist of an even number of 'a'...
23. ### Understanding Set Notation: Exploring the Relationship Between Sets S and W

Ok, I'm not very familiar with set notation. I was just wondering if the following is correct notation and means what I think: {x\inS : \existsy\inx, y\inW} S is a set of pairs of symbols (tuples of length 2 is the technical term I believe). W is a set of symbols. What I want is the...
24. ### Basic set notation question.

G'day all, If i let S={[aij]nxn, where aij = aji, n\inZ+} How do I distinguish between a single natural number n or all natural numbers? I am trying to show that for each n, this set makes a subspace, but am not sure how to represent this set without the ambiguity, as this is not a subspace...
25. ### Proving Power Set Notation: Let B \subseteq U

my actual problem is to let B be a subset of the set U and prove P(B^{C}_{U}) \neq (P(B))^{C}_{P(U)} but I am confused on the scripts and not quite sure what they are wanting me to do i have Let B \subseteq U where B = {b} and U = {B} I know P(B) = {empty set, {b}} and P(U) = {empty...
26. ### Set Notation Question Very Easy

Homework Statement If the domain of a function was defined for all reals except undefined at say x=3 were there was a vertical asymptote would you right (-infinity, 3)U(3, infinity) I'm not sure if it is union or infinity it's union right because technically they don't intersect right...
27. ### Set notation (union and intersection)

Homework Statement Find simpler notation for the two sets: A= \bigcup^{\infty}_{j=0}[j,j+1] and B= \bigcap_{j \in Z}(R minus\ (j,j+1)) Homework Equations The Attempt at a Solution Not really sure what it means by "simpler notation"... Does A=R since the union of...
28. ### Describing all unique 2-tuples from a set using Set Notation

Describing certain 2-tuples from a set using Set Notation How do you describe, using set notation, a certain set of n-tuples generated from a set satisfying the following conditions Condition 1: non of the components of an individual n-tuple can equal each other Condition 2: if (a,b) is...
29. ### Writing a r.v. in set notation

The definition I have for a random variable is X=\lbrace \omega \in \Omega \vert X(\omega) \in B \rbrace \in F where F is a sigma algebra and B is a Borel subset of R. Using function composition, how would one write a similar set notation definition for f(X), where f is a Borel measurable...
30. ### Set Notation in Probability: Clarifying the Meaning of Union and Intersection

I'm having a little difficulty understaning the notation used in my probability class. Would someone tell me if I'm on the right track with it :) A\cup B is the event "either A or B or both." Does this mean that A and B can happen together and that A or B can happen alone? A\cap B...
31. ### Finding Range of Set: Notation & Shorthand

*Suppose I want to find the range of the set \left\{ {t_1 ,t_2 , \ldots ,t_n } \right\} , that is, the difference between the maximum and minimum values (of the elements that is!) in the set. Do I have to fully write out, \max \left\{ {t_1 ,t_2 , \ldots ,t_n } \right\} - \min \left\{ {t_1...