Testing Approximate Equality

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You know how sometimes you have two numbers that are pretty close but not exactly the same? Well, don’t worry we’ve got your back with this handy tutorial on how to test for approximate equality.

To set the stage: why do we need to test for approximate equality instead of just checking if they’re equal or not? Well, sometimes numbers aren’t exact due to rounding errors or other factors that make them slightly different from what you might expect. In those cases, testing for approximate equality can help us determine whether the difference between two values is significant enough to matter in our calculations.

So how do we test for approximate equality? Well, there are a few methods out there, but one of the most common involves using an epsilon value that’s just a fancy way of saying “a small number.” We choose this epsilon value based on what level of accuracy we need in our calculations.

For example, let’s say we have two numbers: 3.14 and 3.141592653589793. If we set our epsilon to be 0.000000000000001 (which is really, really small), then these two values are approximately equal within that level of accuracy.

Here’s how you can test for approximate equality using Python:

# Define a function named approx_equal that takes in three parameters: x, y, and epsilon
def approx_equal(x, y, epsilon):
    # Check if the absolute value of the difference between x and y is less than epsilon
    if abs(x - y) < epsilon:
        # If the condition is met, return True
        return True
    else:
        # If the condition is not met, return False
        return False

# The purpose of this function is to test for approximate equality between two numbers within a given level of accuracy, as determined by the epsilon value.

This function takes in three arguments: `x`, which is the first number we’re testing; `y`, which is the second number we’re testing; and `epsilon`, which is our chosen level of accuracy. The function returns a boolean value (True or False) based on whether the difference between `x` and `y` is less than `epsilon`.

So let’s say we want to test if 3.14 and 3.141592653589793 are approximately equal within an epsilon of 0.00000000000001:

# Function to check if two numbers are approximately equal within a given epsilon
def approx_equal(x, y, epsilon):
    # Calculate the difference between x and y
    difference = abs(x - y)
    # Check if the difference is less than the given epsilon
    if difference < epsilon:
        # If the difference is less than epsilon, return True
        return True
    else:
        # If the difference is greater than or equal to epsilon, return False
        return False

# Test the function with two numbers and an epsilon value
approx_equal(3.14, 3.141592653589793, 0.00000000000001)

# Output: True

With this handy function and a little bit of math knowledge, we can test for approximate equality in our calculations with ease.

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