Question

Use inequality notation to describe the subset of real numbers.The person's age \(A\) is at least 35 .

Short answer

In inequality notation, the age 'A' being at least 35 is represented as \(A \geq 35\).

Step-by-step solution

Formulate the Inequality

According to the provided information, it is known that the person's age (A) is at least 35. This means that 'A' can be equal to 35 or greater than 35. Therefore, in inequality notation, this can be expressed as \(A \geq 35\). This inequality shows all the possible ages 'A' can be, which is equal to or more than 35.

Key concepts

Real Numbers

Real numbers are all the numbers you can find on the number line. They include a wide array of numbers we use in everyday math and science. To give a more comprehensive view, real numbers include several types of numbers:

• Integers: These are whole numbers and their negatives, such as -3, 0, 7.
• Rational numbers: Numbers that can be expressed as the fraction of two integers, for example, 1/2 or -4/3.
• Irrational numbers: Numbers that cannot be written as a simple fraction, like √2 or π.
• Whole numbers: Non-negative integers, such as 0, 1, 2, 3.

Real numbers form a basis for many mathematical calculations and are used to define subsets using inequalities, like our example where we explore ages 35 and above.

Subset

A subset is a smaller group of elements taken from a larger set. When discussing subsets, we are looking at a portion of a larger set that satisfies certain conditions. For example, consider:

• The set of all ages of people, which is a part of the set of real numbers.

When you are tasked to find the ages of people 35 years old and older, you're looking at a subset of all the ages. Our condition is that these ages are at least 35. In mathematical terms, this subset satisfies the inequality condition, just like the one described in the original exercise: ages that are ≥ 35. This subset includes all real numbers starting from 35 and continuing to infinity.

Inequality

Inequality means comparing two values, where one might be less than, more than, or just not equal to the other. When it comes to mathematics, inequalities are a way to demonstrate the relative size between two values. Here’s what you need to know:

• Greater than (>), implies a number is larger than the other, for example, 5 > 3.
• Less than (<), signifies a number is smaller than the other, such as 2 < 4.
• Greater than or equal to (≥), indicates a number is either greater or equal, for instance, A ≥ 35. In our exercise, age 35 or more fits with this inequality.
• Less than or equal to (≤), expresses a number is smaller or equal.

In practical terms, inequalities define a range of values or quantities, helping us understand constraints like age limits or budget limits.

Mathematical Notation

Mathematical notation refers to the symbols used to provide a written framework for mathematical reasoning and computation. It's a specialized language for talking about numbers and their relationships. Here are some key aspects:

• Variables: Letters like 'A' often represent numbers or quantities in equations or inequalities.
• Symbols: Mathematical notation includes various symbols like ≥, <, +, -, and =.
• Equations: Equations use these symbols to define equalities, like 2x + 3 = 7.
• Inequalities: As seen in our topic, they utilize symbols like ≥ to express relationships that aren’t exactly equal.

Each symbol and letter represents a precise idea or relationship, allowing mathematicians and students to convey complex ideas simply and effectively. In the exercise provided, the notation "A ≥ 35" translates the English statement "A person’s age is at least 35" into a clear mathematical form.