Since we want “” we want to be strictly (since we have a parenthesis) larger than and less than “”. But clearly any number is less than infinity, so we can simplify this to just “ strictly larger .” We then just need to put it in the correct format with the braces and using the correct inequality sign!.
1 : Which of the following is equivalent to: ?
Set notation should have the open brace and then the dummy variable (usually with
what kind of number it is) hence the “” above is saying “the set of all , 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 “” is saying “the set of all , a real number, such that is strictly
larger than .”
2 : Which of the following is equivalent to: ?
Remember that strict inequalities (i.e. “” or “”) need parenthesis and non-strict (i.e.
“” or “”) inequalities use brackets. You also need to account for both endpoints. So if
you are trying to interpret then you need “ strictly larger than ”, you would want
the interval ; the initial “” is because it is a strict inequality, and the “” is
because you need the other “endpoint” (which, since we want “anything
bigger than ”, 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”).
3 : Which of the following is equivalent to: ?
Since we want “” we want to be strictly (since we have a parenthesis) larger
than and less than “”. But clearly any number is less than infinity, so we
can simplify this to just “ strictly larger .” We then just need to put it in
the correct format with the braces and using the correct inequality sign!.
4 : Which of the following is equivalent to: ?
Remember that strict inequalities (i.e. “” or “”) need parenthesis and non-strict (i.e.
“” or “”) inequalities use brackets. You also need to account for both endpoints. So if
you are trying to interpret then you need “ strictly larger than ”, you would want
the interval ; the initial “” is because it is a strict inequality, and the “” is
because you need the other “endpoint” (which, since we want “anything
bigger than ”, 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”).
5 : Which of the following is equivalent to: ?
Since we want “” we want to be strictly (since we have a parenthesis) larger
than and less than “”. But clearly any number is less than infinity, so we
can simplify this to just “ strictly larger .” We then just need to put it in
the correct format with the braces and using the correct inequality sign!.
6 : Which of the following is equivalent to: ?
Remember that strict inequalities (i.e. “” or “”) need parenthesis and non-strict (i.e.
“” or “”) inequalities use brackets. You also need to account for both endpoints. So if
you are trying to interpret then you need “ strictly larger than ”, you would want
the interval ; the initial “” is because it is a strict inequality, and the “” is
because you need the other “endpoint” (which, since we want “anything
bigger than ”, 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”).