Comparison and Logic

Operator Precedence Order

In programming, computers execute operations based on a specific precedence order. Imagine it like mathematical rules where multiplication is performed before addition. Python has similar rules for all its operators.

When you write complex expressions, Python will evaluate operators with higher precedence first. If multiple operators have the same precedence, evaluation is done from left to right.

Comparison Operators

Comparison operators are used to compare two values and produce boolean values (True or False). Comparison operators available in Python:

• == equal to
• != not equal to
• < less than
• <= less than or equal to
• > greater than
• >= greater than or equal to

Comparison operators have important characteristics: they compare values of two objects, objects don't have to be of the same data type, all comparison operators have the same precedence, and they always produce True or False values with type bool.

# Example of comparison operator usage>>> 4 == 5False>>> 3 > 2.1  # integer 3 is promoted to float for comparison with 2.1True

Boolean Operators

Boolean operators allow you to combine multiple conditions or modify boolean values. Python provides three main boolean operators:

1. Operator and returns the first value if it's false, or the second value if the first value is true.

2. Operator or returns the first value if it's true, or the second value if the first value is false.

3. Operator not differs from and and or operators because it always produces a new boolean value.

# Example of boolean operators>>> 4.0 and 5.0  # evaluates 4.0 as true, evaluates 5.0 as true, returns 5.05.0>>> 0 and 5  # evaluates 0 as false, returns 0 (short-circuit)0>>> 4.0 or 5.0  # evaluates 4.0 as true, returns 4.0 (short-circuit)4.0>>> 0 or 5  # evaluates 0 as false, evaluates 5 as true, returns 55>>> not 4.0  # evaluates 4.0 as true, returns FalseFalse>>> not 0  # evaluates 0 as false, returns TrueTrue

The and and or operators use short-circuit evaluation, meaning evaluation stops when the result can be determined without evaluating all operands. Both return the last evaluated argument, while the not operator always creates a new boolean value.

Values in Boolean Context

Python has special rules for determining which values are considered False or True in boolean context.

Falsy and Truthy Values

Values considered False (Falsy):

1. False itself
2. None (from NoneType)
3. Zero from all numeric data types:
   • 0 (integer zero)
   • 0.0 (float zero)
   • 0j (complex zero, where j is the imaginary unit)
4. Empty string ""
5. Empty containers: [], {}, (), set()

Values considered True (Truthy):

1. All other values

Boolean Data Type

The bool type in Python represents truth values False and True, is a subtype of integer (int), and booleans behave like 0 and 1 in mathematical operations.

# Bool constructor and arithmetic operations>>> bool(-1)True>>> bool(0.0)False>>> True + True2>>> 3 * False0

Combining Operators

You can combine comparison operators with boolean operators to create more complex conditions. Python also allows more natural comparison chaining like 1 < 2 < 3.

# Example of operator combination>>> 4.0 > 3 and 2 >= 3  # ⇔ True and FalseFalse>>> 7 < 6 or 4 != 2  # ⇔ False or TrueTrue>>> not 0 < 2  # ⇔ not (0 < 2) ⇔ not TrueTrue# Comparison chaining>>> 1 < 2 < 3  # ⇔ (1 < 2) and (2 < 3)True>>> 5 <= 7 < 10  # ⇔ (5 <= 7) and (7 < 10) --- application: interval testTrue

Floating Point Number Comparison

Comparing floating point numbers requires special attention due to precision limitations in digital representation. Loss of precision can cause unexpected results.

Float Precision Issues

# Floating point precision problem>>> a = 0.01>>> b = 0.1**2  # b is 0.010000000000000002>>> a == bFalse# Solution with math.isclose()>>> import math>>> math.isclose(0.01, 0.1**2)True>>> math.isclose(100, 95, rel_tol=0.05)  # relative tolerance is 5%True>>> math.isclose(100, 95, abs_tol=5)  # absolute tolerance is 5True

Solution with math.isclose()

Python provides the math.isclose(a, b, rel_tol=1e-09, abs_tol=0.0) function to test approximate equality. This function uses relative tolerance (rel_tol) and absolute tolerance (abs_tol) to determine whether two values are close enough.

Avoid comparing floating point with == or !=. Use math.isclose(a, b) to test approximate equality. Use abs_tol if one of the numbers is close to zero.