# How to write an inequality in set builder notation

Such problems will continue to present themselves throughout secondary school. The Real Number Line. The most intuitive way is to use the real number line.

## Inequalities. Set Notation etc.

If we draw a line, designate a point on the line to be zero, and choose a scale, then every point on the line corresponds uniquely to a real number, and vice versa: The real number line "respects" the order of the real numbers.

A bigger number will always be found to the right of a smaller number. We visualize a set on the real number line by marking its members. It is standard to agree on the following conventions: To include an endpoint, we "bubble it in. Here is the set of all real numbers greater than -2 and less than or equal to 5: The number -2 is excluded from the set, so you see an "empty bubble"; the number 5 is included in the set, so the bubble at 5 is "filled in.

The set does not need to be "connected. The following is a description of the set of all real numbers with the exception of -1 and 2: Interval notation translates the information from the real number line into symbols.

Our example becomes the interval -2,5]. To indicate that an endpoint is included, we use a square bracket; to exclude an endpoint, we use parentheses. Our example is written in interval notation as. The infinity symbols " " are used to indicate that the set is unbounded in the positive or negative direction of the real number line.

Therefore we always exclude them as endpoints by using parentheses. If the set consists of several disconnected pieces, we use the symbol for union " ": How could we write down in interval notation? There are three pieces to consider: An interval such aswhere both endpoints are excluded is called an open interval.

An interval is called closed, if it contains its endpoints, such as.

## All The Numbers?

An unbounded interval such as is considered to be open; an interval such as is called closed even though it does not contain its right endpoint. The whole real line is considered to be both open and closed.

So intervals are not like doors, they can be open and closed at the same time. The most flexible and complicated? Sets are delimited by curly braces. You can write down finite sets as lists. For instance is the set with the three elements -1, and. For sets with infinitely many elements this becomes impossible, so there are other ways to write them down.

Special symbols are used to denote important sets: N is the set of natural numbers 1, 2, 3, Z denotes the integers 0, 1, -1, 2, -2, Q denotes the set of rational numbers fractions.

R denotes the set of all real numbers, consisting of all rational numbers and irrational numbers such as. C denotes the set of all complex numbers. Beyond that, set notation uses descriptions: The set is the set of all integers exceeding -3 and not greater than 5; this is a finite set; we could write it as a list, The set is even smaller; it contains only five elements: Here are some more examples:§ Implementation of Texas Essential Knowledge and Skills for Mathematics, High School, Adopted (a) The provisions of §§ of this subchapter shall be .

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The most flexible (and complicated?) way to write down sets is to use set notation. Sets are delimited by curly braces. You can write down finite sets as lists. For instance is the Write down the set of solutions to the inequality in all three notations.

Answer. [Trigonometry] [Complex Variables] [Differential.

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