Set notation should have the open brace and then the dummy variable (usually with what kind of number it is) hence the “$\{x \in \mathbb {R}$” above is saying “the set of all $x$, a real number”. The colon should be translated as a “such that” and what follows is the condition that the variable needs to adhere to, followed by the closing brace. Thus for example: the set “$\{x \in \mathbb {R}: x > 3\}$” is saying “the set of all $x$, a real number, such that $x$ is strictly larger than $3$.”

Since we want “$(\sage {p1c1}, \infty )$” we want $x$ to be strictly (since we have a parenthesis) larger than $\sage {p1c1}$ and less than “$\infty$”. But clearly any number is less than infinity, so we can simplify this to just “$x$ strictly larger $\sage {p1c1}$.” We then just need to put it in the correct format with the braces and using the correct inequality sign!.

Remember that strict inequalities (i.e. “$>$” or “$<$”) need parenthesis and non-strict (i.e. “$\leq$” or “$\geq$”) inequalities use brackets. You also need to account for both endpoints. So if you are trying to interpret $x > 5$ then you need “$x$ strictly larger than $5$”, you would want the interval $(5,\infty )$; the initial “$($” is because it is a strict inequality, and the “$\infty$” is because you need the other “endpoint” (which, since we want “anything bigger than $5$”, must be infinity since there is no upper bound given; note that infinity always gets a parenthesis since we don’t include it as a “number”).

Since we want “$(\sage {p3c1}, \infty )$” we want $x$ to be strictly (since we have a parenthesis) larger than $\sage {p3c1}$ and less than “$\infty$”. But clearly any number is less than infinity, so we can simplify this to just “$x$ strictly larger $\sage {p3c1}$.” We then just need to put it in the correct format with the braces and using the correct inequality sign!.

Remember that strict inequalities (i.e. “$>$” or “$<$”) need parenthesis and non-strict (i.e. “$\leq$” or “$\geq$”) inequalities use brackets. You also need to account for both endpoints. So if you are trying to interpret $x > 5$ then you need “$x$ strictly larger than $5$”, you would want the interval $(5,\infty )$; the initial “$($” is because it is a strict inequality, and the “$\infty$” is because you need the other “endpoint” (which, since we want “anything bigger than $5$”, must be infinity since there is no upper bound given; note that infinity always gets a parenthesis since we don’t include it as a “number”).

Since we want “$(\sage {p5c1}, \infty )$” we want $x$ to be strictly (since we have a parenthesis) larger than $\sage {p5c1}$ and less than “$\infty$”. But clearly any number is less than infinity, so we can simplify this to just “$x$ strictly larger $\sage {p5c1}$.” We then just need to put it in the correct format with the braces and using the correct inequality sign!.

Remember that strict inequalities (i.e. “$>$” or “$<$”) need parenthesis and non-strict (i.e. “$\leq$” or “$\geq$”) inequalities use brackets. You also need to account for both endpoints. So if you are trying to interpret $x > 5$ then you need “$x$ strictly larger than $5$”, you would want the interval $(5,\infty )$; the initial “$($” is because it is a strict inequality, and the “$\infty$” is because you need the other “endpoint” (which, since we want “anything bigger than $5$”, must be infinity since there is no upper bound given; note that infinity always gets a parenthesis since we don’t include it as a “number”).