What is the difference between 13 ∈ { n² + n⎮n ∈ Z} and 13 ∈ {n ∈ Z⎮n² + n}
and is 13 ∈ { n² + n⎮n ∈ Z} true? (Z is the set of all integers)
There was a question on my exam today asking if 13 ∈ { n² + n⎮n ∈ Z}. The question seemed to easy, I thought I was missing something.
and is 13 ∈ { n² + n⎮n ∈ Z} true? (Z is the set of all integers)
There was a question on my exam today asking if 13 ∈ { n² + n⎮n ∈ Z}. The question seemed to easy, I thought I was missing something.
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Usually set builder notation has the form { A | B}, where the set consists of all objects of form A under the restriction given by condition B.
{ n² + n⎮n ∈ Z} is the set of all numbers of the form n² + n under the restriction that n is an integer.
{n ∈ Z⎮n² + n} isn't a reasonable description of a set, since "n² + n" isn't a restriction in any sense. There's no *verb*, like ">" or "=" or something akin to that.
As for your question, 13 is not expressible as n² + n for integer n. Solving 13=n² + n would reveal that.
{ n² + n⎮n ∈ Z} is the set of all numbers of the form n² + n under the restriction that n is an integer.
{n ∈ Z⎮n² + n} isn't a reasonable description of a set, since "n² + n" isn't a restriction in any sense. There's no *verb*, like ">" or "=" or something akin to that.
As for your question, 13 is not expressible as n² + n for integer n. Solving 13=n² + n would reveal that.
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The set {n² + n⎮n ∈ Z} means "all numbers of the form n² + n, where n is an integer".
The notation {n ∈ Z⎮n² + n} can only mean the same thing. I tend to read the vertical bar as "...such that...", so I prefer the first version personally.
As for whether the statement 13 ∈ {n² + n⎮n ∈ Z} is true, no it isn't. The expression n² + n can be written n(n + 1), so the statement claims that 13 is the product of two consecutive integers. Since 13 is prime, this must be false.
The notation {n ∈ Z⎮n² + n} can only mean the same thing. I tend to read the vertical bar as "...such that...", so I prefer the first version personally.
As for whether the statement 13 ∈ {n² + n⎮n ∈ Z} is true, no it isn't. The expression n² + n can be written n(n + 1), so the statement claims that 13 is the product of two consecutive integers. Since 13 is prime, this must be false.