Set Builder Notation Puns

How is “-1 ≤ x < 12” written in set-builder notation?

R= {(x,y)|y=-∛x}

I'm trying to identify whether the given relation is a function or not. Cube root has only one real root, so the notation is a function (by 1-1 correspondence) if all elements are real numbers.

However, it is a different case if the notation can imply that complex numbers can be involved. After all, if x and y are allowed to be complex, then there are three values for y when x ∈ ℝ.

How do I interpret the given notation? Can the notation imply that complex numbers can be involved? I've searched that complex numbers can be in a form of ordered pair as (x,y) so I think the notation can include complex numbers. But I'm still not sure...

Thank you for your help!

I know in interval notation you can simply write (-infinity, infinity) but how do you represent the same thing in set builder notation? I cannot find it on Google. There's a thousand tutorials on using set builder but I don't see how to represent negative infinity to infinity.

Is it {x|x€R}?

Hello

1)My book asks if it's possible to write every set by enumeration. I thought it's possible for countable set and impossible for uncountable sets. But practically how could I write N by roster method? Would just N={0,1,2...} be correct? And Z={...-2,-1,0,1,2...}?

2. I remember someone saying that A={x^2 s.t x€N} is writing a set by enumeration. Why that?

Thank you in advance

I've got 3 roots for me to show the domain, and I only can denote it as such:

Interval Notation : (-∞,-3) U (1,5)

Inequality Notation : -∞ < x < -3 , 1< x < 5

How do I write it as set builder notation?

I understand set builder notation mostly but I’m a little confused abt this question:

Write the following set using the set builder notation. (3) Set P of all rational numbers between -2 (included) and 7 (excluded)

Since 7 is excluded is it x| x is an element of Q, and x is more than or equal to -2 and x is less than or equal to 6?

I can’t write the appropriate symbols on my phone so sorry if it looks confusing

I'm working on a grammar and parser of mathematical syntax, and I've come across an ambiguity which I'm unsure how to resolve. There is a conflict between the current feature set:

1. Implicit multiplication lets x y parse as x*y
2. Absolute value, x |y| parses as x*abs(y)
3. Set enumerations, {1, 2, 3}
4. Set-builder notation, {x : x > 0}
5. Set-builder convention also uses a bar: {x | x > 0}, or even {x | |x| > 3}

(4) works great, but (5) causes the recursive descent parser to start processing the bar as in (2), i.e. the start of implicit multiplication by an absolute value. I know this isn't a true ambiguity since there can only be one set-builder bar at this nesting level of braces, and the set-builder bar must be the leftmost bar. I am worried that arbitrary lookahead is required. Is this a common problem, or is there an elegant solution?

I understand the logic of it but I'm having trouble translating it into a proof. Labeling laws would also really help!

Hi r/math! I was reading through the Rudin chapter on The Lebesgue Theory, and came across the "introduction" of the notation ({x|P}) as denoting the set of (x) having property (P). Given that this is, at least to my knowledge, fairly standard notation, I got to wondering when the earliest use of such notation was? Are there any historians here who can help me out?

What is the set builder notation for this sequence? I just started a Mathematical Structures class and I keep getting stuck on things like this and wanting to give up. Help!

Hey all, I'm doing set theory and have a school question that wants a set builder answer for "the first 10 integers starting from 4, divisible by 3". I've answered it as:

$A = \{n \in \mathbb{Z} | \frac{n}{3} \in \mathbb{Z} \land 4 < n \le 33\}$

I think this is right and should have a cardinality of 10 - But my problem with it is the sentiment of "The first 10 integers" isn't quite there, it just happens to be the first 10 because I'm limiting the n - If I changed the n / 3 in Z to n / 4 in Z, it wouldn't remain a set of 10 values, I'd have to also adjust the last bit to be <= to 40 (or something) as well.

So my question is: Is there a set-builder construct that better denotes "The first 10 values of this set"? Or am I stuck with being slightly implicit? Could I literally just write "The first 10 values" seeings as this is basically pseudocode anyway?

Thanks!

In many examples, I see things like:

{ x ∈ ℝ | x > 5 }

Why not say:

{ x | x ∈ ℝ & x > 5 }

Or are both okay?

P : D→{TRUE, FALSE} may be written (D, S), where S = {a ∈ D| P(a) = TRUE}

In this case, what is the output of 'S'? I am trying to wrap my head around this type of notation. If S can only equal the sequence of a's in D in which P(a) is TRUE, how does that help identify the predicate of D? Wouldn't it just output a list of D's? This is a rock paper scissors example, for context. If D = {ROCK, PAPER, SCISSORS} then wont S just be {SCISSORS, ROCK, PAPER} but since order doesn't matter in a set, isn't S arbitrary? It doesn't tell us anything at all, other than the outputs are one of the inputs. How is [P : D→{TRUE, FALSE}] connected at all to (D,S)?

http://puu.sh/dgajq/8ab805af0b.jpg

function of t = the square root of -2t + 7

Does it matter which condition is on which side of the : or |? i.e. Is {(x,y) in R^(2) : y=x^(2)-2} the same as {y=x^(2)-2 :(x,y) in R^(2)}?

(PS I know to use the "exists in" symbol, not "in" - just on phone)

I never learned any of them and I'd like an intro to both. Thank you!