When do we need to use float.PositiveInfinity and float.NegativeInfinity?

Question

When do we need to use the Infinity values, kindly add a real-world sample if available.

Answer 1

For example, negative infinity is a natural maximum value of an empty list. With this, you have: max(l1 + l2) = max(max(l1), max(l2)), where l1 and l2 are arbitrary lists, possibly empty.

A real-world application of this principle:

float Max(IEnumerable<float> list)
{
    // invariant: max contains maximum over the part of the list
    // considered so far
    float max = float.NegativeInfinity;
    foreach (float v in list)
        if (v > max)
            max = v;
    return max;
}

Answer 2

PostiveInfinity

This constant is returned when the result of an operation is greater than MaxValue.

NegativeInfinity

This constant is returned when the result of an operation is less than MinValue.

So you would use these constants to verify that your values are out of range for their type.