MHB Question ' write the elements of set A'

[mathlearn]

Any ideas on how to begin

Many thanks :)

 

[I like Serena]

Any ideas on how to begin

Many thanks :)

Hi mathlearn! (Smile)

To be honest, that looks like some kind of typo in the problem statement.If we read it like:
$$A=\{x \mid x \in \mathbb Z^+, \mathbb Z > x - 3 \}$$
then it would or should mean that $x-3$ is smaller than any element of $\mathbb Z$, which is never the case.
In that case $A$ is the empty set ($\varnothing$).Alternatively, if we read it as:
$$A=\{x \mid x \in \mathbb Z^+, z > x - 3 \}$$
where $z$ is some number that is presumably in $\mathbb Z^+$, then we have $0<x < z+3$.
So in that case the elements of $A$ are $1, 2, ..., z+2$.

 

[mathlearn]

Hi mathlearn! (Smile)

To be honest, that looks like some kind of typo in the problem statement.Alternatively, if we read it as:
$$A=\{x \mid x \in \mathbb Z^+, z > x - 3 \}$$
where $z$ is some number that is presumably in $\mathbb Z^+$, then we have $0<x < z+3$.
So in that case the elements of $A$ are $1, 2, ..., z+2$.

Reading it in Set builder method

"The set of all x such that x is a positive integer, where z is some number positive number greater that x - 3"

so z(a positive integer,this case 1)> 1-3 = -2-------------------(✖ not a positive integer)
z(a positive integer,this case 2)> 2-3 = -1-------------------(✖ not a positive integer)
z(a positive integer,this case 3)> 3-3 = 0-------------------(✖ neither negative nor positive)
z(a positive integer,this case 4)> 4-3 = 1-------------------(✔ a positive integer)
z(a positive integer, this case 5)> 5-3 = 2-------------------(✔ a positive integer)

and so on like I like Serena ; the numbers are 1,2,3,4,5... on

Representing in a number line,

OR

A=$\left\{1,2,3,4,5,6,...\right\}$

Correct I guess?

Many Thanks :)

 

[Evgeny.Makarov]

Alternatively, if we read it as:
$$A=\{x \mid x \in \mathbb Z^+, z > x - 3 \}$$
where $z$ is some number that is presumably in $\mathbb Z^+$, then we have $0<x < z+3$.
So in that case the elements of $A$ are $1, 2, ..., z+2$.

Reading it in Set builder method

"The set of all x such that x is a positive integer, where z is some number positive number greater that x - 3"

Even though ILS said that $z$ is presumably in $\mathbb Z^+$, one cannot be certain this is the case. I recommend contacting the problem author and clarifying the problem statement. I don't have high confidence in a problem statement that uses the euro symbol instead of $\in$ and uses the same symbol $Z$ for a set and an individual number.

so z(a positive integer,this case 1)> 1-3 = -2-------------------(✖ not a positive integer)
z(a positive integer,this case 2)> 2-3 = -1-------------------(✖ not a positive integer)
z(a positive integer,this case 3)> 3-3 = 0-------------------(✖ neither negative nor positive)
z(a positive integer,this case 4)> 4-3 = 1-------------------(✔ a positive integer)
z(a positive integer, this case 5)> 5-3 = 2-------------------(✔ a positive integer)

and so on like I like Serena ; the numbers are 1,2,3,4,5... on

The set consists not of $z$s, but of $x$s. The number $z$ has to be given up front, before we consider the definition of set $A$. As ILS wrote, once $z$ is given, $A=\{1,2,\dots,z+2\}$.