Express the set $x \geq 2$ using interval notation.
Answer (2)
The set includes all real numbers greater than or equal to 2.
Use a square bracket '[' to include 2.
Use a parenthesis ')' with infinity.
The interval notation is [ 2 , ∞ ) .
Explanation
Understanding the Problem We are asked to express the set xg e 2 using interval notation. This means we need to represent all real numbers that are greater than or equal to 2 as an interval.
Determining the Interval Boundaries The set xg e 2 includes all numbers starting from 2 and extending indefinitely to positive infinity. In interval notation, we use square brackets to include the endpoint and parentheses to exclude the endpoint or infinity.
Applying Interval Notation Since x can be equal to 2, we include 2 in the interval using a square bracket '['. Infinity is not a number, but a concept representing unboundedness, so we always use a parenthesis ')' with infinity.
Final Answer Therefore, the interval notation for the set xg e 2 is [ 2 , tt y ) .
Examples
Interval notation is used in various fields, such as calculus and real analysis, to describe sets of numbers. For example, when describing the domain or range of a function, interval notation provides a concise way to represent the set of all possible input or output values. In real life, you might use interval notation to describe a range of acceptable temperatures for a chemical reaction or a range of possible values for a measurement in an experiment. Understanding interval notation helps in clearly communicating and working with sets of numbers in mathematical and practical contexts.
The interval notation for the set x ≥ 2 is [ 2 , ∞ ) . This notation indicates that the set includes all real numbers starting from 2 and extending indefinitely to positive infinity. We use a square bracket for 2 to show it is included and a parenthesis for infinity to denote it is not a specific number.
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