Comparing Numbers for Approximate Equality

Approximate equality between two real numbers is determined by checking whether their absolute difference is within a specified tolerance (epsilon).

• Uses a tolerance (epsilon) to handle floating-point precision issues.
• Calculates the absolute difference between the two numbers.
• Returns true if the difference is less than epsilon; otherwise, returns `false.

The following examples illustrate approximate number comparison using different values and tolerance levels.

Example 1: Compares two decimal numbers using a larger tolerance value.

const isApprox = (num1, num2, epsilon) => {
    // Calculate the absolute difference
    // and compare it with epsilon
    return Math.abs(num1 - num2) < epsilon;
};

console.log(isApprox(10.3, 10.1, 0.5));

true

Example 2: Compares a mathematical constant with its approximate decimal value.

const isApprox = (num1, num2, epsilon) => {
    // Calculate the absolute difference
    // and compare it with epsilon
    return Math.abs(num1 - num2) < epsilon;
};

console.log(isApprox(Math.PI / 2.0, 1.5708, 0.004));

true

Example 3: Compares two numbers whose difference exceeds the specified tolerance.

const isApprox = (num1, num2, epsilon) => {
    // Calculate the absolute difference
    // and compare it with epsilon
    return Math.abs(num1 - num2) < epsilon;
};

console.log(isApprox(0.003, 0.03, 0.004));